QUESTION 4 x' = 12 t2 x, x(0) = 3 Solve the above IVP and then find x(0.5). Put x(0.5) accurately calculated to the nearest thousandth (3 decimal places). Notation: dx and x = x(t) dt x' = %3D

Q: dy Solve the differential equation = ex-y +e +e+1 dx O e +y = e* + x + C In(e + 1) = e* + x + C O…

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Q: Question 4 4 Solve the first order equation (323 +2xy)dx +C x4+2y) dy =0

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Q: (b) Figure 2 shows the experiment conducted to study the relationship between the velocity of blood…

A: Solve the problem as shown below.

Q: Question 4 SN Given the differential equation (5x² - y²) dx + 2ydy = 0, What is dx 01 0-1 00 O-2y =?…

A: Given the differential equation : (5x²-y²)dx+2ydy=0

Q: Question 5: Solve the following differential equation by using laplece transform method X" + 2x + 2X…

A: Convert the equation to Laplace transform:…

Q: Question 2 Given a differential equation as d²y dy 2². - -3x- +3y=0. dx² dx By using substitution of…

A: Let's solve diffrential equation by using substitution x=e^t  or t=ln(x).

Q: Question 13. Use variation of parameters to solve the differential equation: 1 y" + 4y : sin 2x

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Q: Question 13 Solve this differential equation: dy 0.05(1000 – y) dt y(0) = 50 y(t) = Submi Question 9…

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Q: QUESTION 2 a) Solve the following differential equation by separation of variables method. 2.xydx +…

A: Given; a) 2xydx+(1+3y2 )dy=0 b)dy/dx +3x2y=6x2.

Q: 27 dy -y COSX solve the differential egdation XP

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Q: The differential equation: a+b+c=0 has a solution given by: x = eat (A sin ßt + B cos ßt) If a = 5,…

A: The given differential equation is ad2xdt2+bdxdt+cx=0; a=5 , b=9, c=8. The given solution is…

Q: i) Solve: (1+ydx = (tan-y-x)dy. %3D ii) Solve; ylogydx + (x- logy)dy = 0.

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Q: QUESTION 3 Find the particular solution for the given separable differential equation. dy 2x+y,…

A: We have to solve differential equation

Q: dy Зх + 2у dx Зх + 2у — 1 ||

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Q: QUESTION 11 A cylindrical shell has a thickness of 0.2 cm. Using differentials, approximate the…

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Q: Question 8 Use differentials to find the approximate value of y: (2x 1)* when x = 0.98. O 0.88 O…

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Q: Question 3: A) Solve the separable equation: dy xe2x-3y. dx %3D B) Solve the initial value problem:…

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Q: QUESTION 1 Verify that y= (x+C)cosx is a solution to the differential equation: y' +ytanx= cosx;…

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Q: QUESTION 1 Consider the IVP: x" + (x')? + 4tx=0, x(0) = 1, x'(0) = 2 Using the Euler method with a…

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Q: Question 3: Find the solution to the exact differential equation e'Iny(y)dz = y(2) = 3 y(z) =???

A: Note: There is one mistake in question because given different equation is exact. So for exact…

Q: Question 5 Determine whether the equation exact. Otherwise, find an integrating factor that will…

A: Topic - differential Equation

Q: Question 7 Determine whether the given differential equation is exact. If it is exact, solve it. dy…

A: First make this equation in the form of Mdx+Ndy=0 then find dM/dy and dN/dx   and if both are equal…

Q: Question 5. Find the answer to the following initial value problem dx+e**dy =0 when y(0) = 0 X+y %3D

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Q: Problem 7 Solve the DE by finding an appropriate integrating factor: (2y + 1)dx + () dy = 0 %3D

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Q: Question 6 Use differentials to find the approximate value of y: (2x 1) when x = 0.98. O (E) None of…

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Q: (x² +1). +3x(y-1)=0, y(0) = 2

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Q: dy Solve the differential equation: e-" (e – e"). dx O ev = (e* + 1) + ce e = (e* – 1) + ce-e. O e =…

A: We have to find Solution of differential equation.

Q: Question 4: Confirm that the function you found is a solution to the differential equation z' + z =…

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Q: Given the following ordinary differential equation   y'=4y What is a solution for  y(x) such that…

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Q: 2 xy' = y+x² sin x, y(7)=0

A: Given differential equation is xy'=y+x2sinx With initial condition.

Q: QUESTION 2 Show that the given differential equation is exact. Hence, solve the differential…

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Q: Question 4 1/2 9 x2 Calculate the integral: dx 3/2 (1 – x²) *2 а) О27у3 - Зл Зл b) 09/3 + 3/3 2 3n…

A: Solution:-

Q: Question 5: Solve the following differential equation use integration method d²y 1) + 2xy = x dx2 2x…

A: 1. d2y/dx2 + 2xy = x 2. d3y/dx3 = 2x3/y

Q: Solve the initial value problem + x = Heaviside (t – 5), x (0) = 14, dt? dx (0) = 2 Important: Use H…

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Q: Given, (+) dæ + ) dy =iß an exact differential equation. Determine the value of A.

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Q: QUESTION 2 A cylindrical shell has a thickness of 0.2 cm. Using differentials, approximate the…

A: Explained below

Q: Question 3 Зу? dy Solve the differential equation dx 1 y(9) %3D 33 y(x) =

A: Use variable separable method

Q: PART C: Determine which of the following differential equation are exact, and solve for general sol…

A: Please refer the attached image for complete solution.

Q: page 6 dy = 4y sin2x, y(0) = 1. Give answer as an explicit function y=f(x). dx 6. Solve the…

A: The differential equation of the form dydx=f(x)g(y) is variable separable form. To solve this type…

Q: (a) Determine whether the following differential equation is exact, if exact then solve 2.xy dx +(1+…

A: The given equation is: 2xy dx+(1+x2)dy=0 Comparing it to P dx+Q dy=0 So,  P=2xy, Q=1+x2Py=2x…

Q: Question 4: Confirm that the function you found is a solution to the differential equation z' + z =…

A: The differential equation is given as z'+z = cos(2t) Corresponding homogeneous equation is given as…

Q: Question 2 Given a differential equation as -3x dy +4y=0. 1 dx² dx By using substitution of x = e'…

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Q: QUESTION 6 The values of n and m for which the differential equatin is exact by+x)dx+(x?ym +y)dy D0

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Q: Question 11. Use the method of undetermined coefficients to solve the differential equa- tion: y" +…

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Q: Question 5 Consider a series circuit consisting of a resistor of R ohms, an inductor ofL henries,…

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Q: Question 4 Each side of an equilateral triangle measures 3cm, with a possible error of 0.1cm. Using…

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Q: Question 2 What is the degree of the differential equation 2³ 4² + x² ( 4 ) ³ + x²y = sin æ 3 3 By…

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Q: Given the following ordinary differential equation y' = 5y What is a solution for y(x) such that it…

A: Solve the given ODE by separation of variables.

Q: 17. An initial population, p, of 10000 bacteria grows in number according to the equation 4t p(t) =…

A:

Differential Equations

Have you ever observed the movement of the satellites and rockets or how the planets go around the sun in their orbits? How will you determine their motion? Definitely they follow some scientific laws and these kinds of problems are framed as differential equations.