Q: Show that the given differential equation is not exact hence solve it 2²ydx – (2³ + y³)dy = 0
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Q: State the case and solve for the general solution of the given special second-ordered differential…
A: We have the differential equation given by yy''+y'2=y'. We now have yy''+y'2=y'⇒yy''+y'y'=y' By…
Q: without solving the undetermined coefficients, the correct form of a particular solution of the…
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Q: Solve for the general solution of the below differential equation. y" + 3y' + 2y = cos x
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Q: Show that the following differential equation is perfect or not, then find its general solution:…
A: Introduction: Any equation with one or more terms is a differential equation. It includes taking the…
Q: For which values of n is the function ya solution of the differential equation xy"-Kxy'-6y=0
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Q: 1 3. y' -- %3D xy+x²y3
A: See the details solution in below
Q: 5) y = 2( 3x + y ) - 1
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Q: 1. Describe the solution of the differential equation ydx – 2xy dy = 0.
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Q: It is known that y = ekt is a solution of the differential equation y″ − 16y = 0. Find the value(s)…
A: Given that,
Q: Consider the following Differential Equation (2) y" – 2 y" – 3 y' = cos(3x) + e ". | Determine the…
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Q: 5. Find the general solution to the differential equation et y" – 2y' + y 1+ x2 (where y' = )
A: Let us consider the differential equation y''+py'+q=g(x) To solve the equation Determine the…
Q: Consider the following differential equation Y = ry /1+x* What is the general solution ?
A: Given differential equation
Q: 5. What is the general solution of the following differential equation ( .6³yod?y =0)? ,d*y +9. dx2…
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Q: (3ху + 3у - 4) dx + (x+1)2dy %3D0
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Q: Find a particular solution to the differential equation y" + Oz/ – 16y = -768t°.
A: Given: y'' + 0y' - 16y = -768t3
Q: If we use the method of undetermined coefficients, the particular solution of the following…
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Q: If we use the method of undetermined coefficients, the particular solution of the following…
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Q: 1. Select the correct type for the following differential equation 2ху + 6х + (x2 - 4) у' 3 0 х # +2
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Q: y= 4 + Inx; xy'
A: Since you have posted multiple questions i can do first question as per our company guidelines…
Q: I. Solve the following manually using separable differential equations method. 3.2xy' = 1+ y?
A: topic - differential equation
Q: Find the solution of the following Differential Equations by Homogenous Equation 6) y'=+x y-x
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Q: 4y" + y' = 0
A: We calculate differential equation by the help of Euler identity
Q: 1. Obtain the differential equation associated with y=Ax2+Bx+C
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Q: Obtain the general solution of the given differential equation: dy = cos²xcosydx
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Q: 2.2y" +y' -y = x + 1 + e¯* when y(0) = 1;y'(0) = 0
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Q: Determine the solutions of the following differential equations using Type IV:
A: Given that: (x2-x-2y+1)dx-xdy=0 and y(1)=12
Q: what is the particular solution to the differential equation dy/dx=3sin(x)(2-y)with the initial…
A: You need to apply variable separable metod to solve the given differential equation.
Q: y' - Зу %3D =x*y/3
A: Given differential equation y' - 3yx = x4y13
Q: 1. y'- = xy2
A: Solution is given below:
Q: 1) Find the general solution of the differential equation. y^(4)-y=4t+cos(t)
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Q: Solve for the General Solution of the given Differential Equation dx – (1+ 2xtany)dy
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Q: If we use the method of undetermined coefficients, the particular solution of the following…
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Q: A. Obtain the differential equation of the given solution by eliminating the arbitrary constant(s):…
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Q: 8 Find the general solution of the differential equation: xy' + y: X Use lower case c for constant…
A: Given : xy'+y=8x+9x Following formulas are used- ∫1xdx=lnx∫xndx=xn+1 n+1
Q: y' = 2( 3x + y )? - 1
A: We will find out the required solution.
Q: 1 3. y'-- %3D ху+x?у3
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Q: 1. (y²+ 6x²)dy –- 4xydx=0
A: The solution is given as
Q: Find the solution of the following Differential Equations by homogenous equation 7) y'=(y-x)
A: Since you have asked multiple questions, we will solve the first question for you. If you want any…
Q: Solve the following 2nd order differential equation by Varition of parameters method. (D2 + 9) y =…
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Q: 3) ( y³ + × )V = 1 x (2) = 1
A: In the given problem initial conditions was wrong it should be y(2) =1 instead of x(2) =1, since 'y'…
Q: Obtain a solution for each of the given differential equations using the metho discussed. 1. (3x –…
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Q: obtain the solution of the following differential equation y'=cos^2x cosy
A: Given differential equation is: dydx=cos2xcosy Use variable separable to get solution of…
Q: 6. xy' +y-x+ xycotx = 0
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Q: , solve the following implicit ordinary differential equations. y tan- y (). 4. y' = -, y (1) = 1 x…
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Q: The value of k that will make the differential equation (6xy³ + cos(y))dx + (2kx²y² - xsin(y))dy = 0…
A: Consider the differential equation: 6xy3+cosydx+2kx2y2-xsinydy=0 Comparing the given differential…
Q: Use the method of variation of parameters to find a particular solution of the following…
A: Given differential equation is, y"+4y=cos8x Auxiliary equation is, m2+4=0m=±2i Then the…
OBTAIN A SOLUTION TO THE FOLLOWING HIGHER ORDINARY DIFFERENTIAL EQUATIONS (MOUC)
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- Cesium-137 has a half-life of about 30 years. If we begin with 200 mg of cesium-137, will it take more or less than 230 years until only 1 milligram remains?Suppose the proportion of all college students who have used marijuana in the past 6 months is p=0.40.ln a class of 150 students that are representative of all college students,would it be unusual for the proportion who have used marijuana in the past 6 months to be less than 0.33? Yes No Cannot be determined. Explain how you made your decision in the above question.The radioactive isotope lead has a half-life of 3.3 hours and decays at a rate proportionate tothe amount present at time t. How long will it take for 90 percent of lead to decay if 1 gramof the isotope is present at the start?
- A radioactive substance decays at a continuous rate of 17% per day. After 8 days, what amount of the substance will be left if you started with 50 mg?Find the first direvative. y ln x - x ln y = 1Suppose the half-life of a certain radioactive substance is 20 days and that there are5 grams present initially. When will there be only 1 gram of the substance remaining?
- The decay of radioactive elements can sometimes be used to date events from Earth’s past. In a living organism, the ratio of radioactive carbon, carbon-14, to ordinary carbon stays fairly constant during the lifetime of the organism, being approximately equal to the ratio in the organism’s atmosphere at the time. After the organism’s death, however, no new carbon is ingested, and the proportion of carbon-14 in the organism’s remains decreases as the carbon-14 decays. Scientists who do carbon-14 dating often use a figure of 5730 years for its half-life. Find the age of a sample in which 10% of the radioactive nuclei originally present have decayed.A certain radioactive material is known to decay at a rate proportional to the amount present. If initially there is 50 mg of the material present, and after 2 hours it is observed that the material has lost 10% of its original mass.A certain cancer among men aged 70 and over occurs at a rate of 1 in 150. A blood test will be positive 99% of the time if the cancer is present, but is also positive 5% of the time if the cancer is not present.
- 3. Ununoctium decays naturally at the rate proportional to the original quantity. If there are 20 grams initially, and after 10 years, 0.6% of the original amount decomposed, design an equation that will represent the amount of remaining element at any given time.A quantity with an initial value of 840 decays continuisly at a rate of 5% per day. What is the value of the quantity after 10 weeks, to the nearest hundredth?3. A new compound called Corpium radioactively decays at the rate of -0.035% every year. If there is initially 500g of it in 2020, how much will remain in 2050?