Question 15 A tank contains 6L (liters) of water in which is dissolved 32 g (grams) of a chemical. A solution containing 2 g/L of the chemical flows into the tank at a rate of 2 L/min, and the well-stirred mixture flows out at the same rate. Give the differential equation that describes the rate of change of the amount X of the chemical in the tank. A dx = 8- dt 3+t dx B 4. dt dx dt 6. dx (D 4. dt 3+t

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 3 Use the method of variation of parameters to solve for the differential equation y" – 6y…

A: The solution is given as

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

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Q: Question 1 dV Solve the following differential equation: de Vcote + V³cosece

A: According to guidelines here solution of only firt question

Q: x +y = x³ /y X-

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Q: Question 3 The solution of the following differential equation if x = 10 when t = 0: 4x (dx/dt) = 7…

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Q: Question 3: Solve the differential equation 3- y = e x >0 dx

A: Since you have asked multiple question, we will solve the first question for you. If you want any…

Q: Help4

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Q: QUESTION 7 Solve the differential equation with initial condition dy = 7y²x³ dx y(2) = 3

A: Given: dydx=7y2x3

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 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: Use for question 1 1. Construct a slope field for the differential equation 2 = x + 2y dx

A: Slope is always dy/dx

Q: Question 9 Solve the following exact differential equation. Ay+25 +13x+26y = C OBy + 15x+28y = C oc…

A: Given that: (x3y2+12)dx+12x4y+25dy=0

Q: Question 3 Use the method of variation of parameters to solve for the differential equation y" – 6y'…

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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 3: Solve the differential equation 3 - y = e7 x > 0

A: By, bartleby policy first question only unless asked otherwise.

Q: If the differential equation ydx+xdy= 0 is being solved, what is the geometrical figure represented…

A: Differential equations

Q: Question 28 Solve for the value of "C" on the given differential equation below. Let y(1)-1

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Q: Question 4 Find the value of y for the given differential equation if the value of the arbitrary…

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Q: Question 3: Solve the differential equation 3-y = es x > 0 dx

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Q: Question 19 SM Given the differential equation y dx + (3xy + y² - 1) dy = 0, What is value of dy 00…

A: As we know that; The differential equation Mdx+Ndy=0 is said to be exact if ∂M∂y=∂N∂x. And The Power…

Q: Question 4 Solve the differential equation. y' + 2xy = 23x A) y = 23 + 2x + ce x2 23 B) y = + ce x2…

A: Given equation is  y'+2xy=23x              (i) It is a first order linear ODE. On comparing the…

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

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Q: (x² – y²) dx + (x² – xy) dy = 0

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Q: Question 2: 1) Solve the following separable differential equation: y' = (9 + 16y²) x²e3x

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

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Q: Question 8 Solve the given differential equation by using an appropriate substitution: = y(xy3 – 1).…

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Q: Question 5 Find the solution of the differential equation y" – 16y = 2e4x

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Q: Problem 18. An object with mass 100 kilograms is released at a height of 500 meters above the ground…

A: First draw the free body digram.. Then balanced the force then.. Put a=dv/dt and v=dx/dt and…

Q: dw 1. Solve the differential equation 4 = -5e+w dt

A: 4dwdt=-5et+w4dwdt=-5(et*ew)4dwew=-5etdt4 e-wdw=-5etdt

Q: Question 14 What is the simplest form of the integrating factor for the differential equation y' +…

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Q: Question 6 Find the solution of the differential equation y" – 4y = 4x – e3x y = C,e2x + C2e-2x + e*…

A: Let's find.

Q: Question 3 dy Solve the linear differential equation, (1+x) +y= cosx, which satisfies the dx (a)…

A: Linear differential equation

Q: QUESTION 5 Find the general solution of the ordinary differential equation y''- 2y'= - 5+e¬2x

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Q: Question 1. Find explicit general solution of the following differential equation. dy +y = 10V. 211r…

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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: Question4: A. Solve the initial value problem (IVP) for the following differential equation xy' +…

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Q: Question 15 Solve the differential equation. y'e 3x + 3ye 3x = 4x A y = 4x 2e 3x + ce 3x B y = 2x 2e…

A: The given differential equation is, y'e3x+3ye3x=4x

Q: One of the following is a solution of the differential equation y"-y=0

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Q: Problem 4: A 200 gram hockey puck was tossed on ice with an initial velocity of 10ms-1. In 2 seconds…

A: Given mdvdt=-kv Initial velocity of 200 gram hockey puck is 10m/s In 2 seconds its velocity is 8m/s…

Q: Question 11 Solve the given differential equation by using an appropriate substitution. dy ху?. = y3…

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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 1 Find the particular solution for the differential equation dy x2-3 = 2(y + dx dy dx'…

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Q: QUESTION 8 Find the solution to the following differential equation dv - = 9.8 – 0.196v dt

A: Basics of Differential equation are used.

Q: Question 2. Solve the given differential equation dy + y = ty. 7 = dt

A: To solve the given differential equation.

Q: Question 4 Solve the following differential equation: (v')? - 10yy' + yy"=0

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Q: If the acceleration A(t) of an object is proportional to the square root of its speed S(t), what is…

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Q: Question 1: Use the Method of Cauchy-Euler to solve the following differential equation: 4t?y" –…

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