3(@) Solve the Linear differential equation dy + ytan z = 2 cosT, given that y(0) = 13 dz (b)Show that given differential equation is exact hence solve it (cos z sin z – ry) dx + y(1 – x²)dy = 0

Q: Kindly use Exact Differential equation to solve this. (y3 - y2sinx - x)dx + (3xy2  + 2ycosx)dy = 0

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Q: VI(v)²-(JxcosVx – sec Vx '= 1

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Q: 6 The differential equation (y+3x)dy + (x-y) dx = 0 is best solved by A. variable separable C. Exact…

A: As per our guidelines we are supposed to answer only first one.  Kindly repost other parts in the…

Q: (e cos y + y)dx + (2y + x – e sin y)dy = 0 -

A: 1)verify that the differential equation bis exact using the test for exactness method   2) find the…

Q: A differential equation is in the form of x"A(y)dy+ B(x,y)(xdy – ydx) = 0 Show that if the function…

A: given xnAydy+Bx,yxdy-ydx=0 to show- if Bx,y is homogenous , then we can solve any differential…

Q: Show that the differential equation (x + y)dx - 2xdy = 0 is homogeneous and then use the…

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Q: Find the general solution for differential equation. Verify that  solution satisfies the original…

A: 4x3-2dydx=0 On simplification, we get ⇒2dydx=4x3⇒dydx=2x3⇒dy=2x3 dx Now integrating on both sides,…

Q: e2" (x + 1) cx – e(x4 – 1)dy = 0 d Hint: 4 (arctan x) = dx 1+x*

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Q: (a) Given a differential equation (2y – cos 2x): + 2x + 2y sin(2x) = 0. dx Identify the exactness of…

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Q: Find the solution of the Differential Equation: dx/dt=cos x cos^2 t

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Q: Show that the differential equation (x + y)dx - 2xdy = 0 is homogeneous and then use the…

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Q: the given differential equation has a particularsolution yp of the form given. Determine the…

A: Given: y'' + y = 2 cos x + sin x, yp= Ax cos x + Bx sin x To Determine: the coefficients in yp and…

Q: Solve this differential equation: 3.) (x+1)dy-2(y+x+1)dx=0; when x=1,y=4

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Q: Obtain the general solution of the differential equation:y’ = cos2x cosy.

A: As per company guidelines we can solve first question. I hope that the given solution will help you.…

Q: Consider the differential equation: (x4 cos y) dy + (x + 3x3 sin y) dx = 0. (a) Show that this…

A: Given: The differential equation: x4cos ydy+x+3x3sin ydx=0.

Q: I. Determine whether the given differential equations are homogenous or not homogenous. If the…

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Q: A. Give two integrating factors for 3(y* + 1)dx + 4xy³dy = 0. One integrating factor must be in…

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Q: For the differential equation 2xy=y -x. i) Explain why we can not find any integrating factor for…

A: Given first order differential equation is:  2xydydx=y2-x2 First order linear differential equations…

Q: 2. The linear differential equation x*dy+(2y-3x²y-x' dx 0 has the integrating factor equal to (Note:…

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Q: Solve the differential equation with appropriate method. Finalize answer free of logarithms,…

A: Here we have to find the solution of given differential equation.

Q: y' = y² - e³xy² subject to initial condition of y(0) = 1

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Q: Consider the differential equation: (x* cos y) dy + (x + 3x sin y) dx= 0. (a) Show that this…

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Q: Find the general solution of the given differential equation. 2 dy dx +6y= 3 y(x) = Give the largest…

A: general solution =complementary solution +particular solution      so find general solution then we…

Q: Find the general solution of separable differential equation:               (x^3+4)dy/dx = (2x^2)y

A: Solved below...

Q: A mass of 50 kg is attached to a spring whose constant is 32 N/m

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Q: y' xe2y subject to initial condition of y(0) = -1 =

A: Please see the below picture for detailed solution.

Q: y^2dx + (x^2 + 3xy + 4y^2)dy = 0; when x = 2 , y = 1

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Q: Find the general solution of the differential equation: (1+cos(I)y-(sin(x)y 2x y'+ sin(a) 1+co6(x),…

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Q: Given a differential equation of y’=ln(x+1) and y(0)=1. Find the value of y when x=1 using Euler’s…

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Q: Find the particular solution of differential equation 3ye" using the given boundary condition: y = 2…

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Q: (x4cos y) dy + (x + 3x3sin y) dx = 0. Show that this differential equation is not exact. Find the…

A: given  (x + 3x3sin y) dx+(x4cos y) dy= 0 to show differential equation is not exact solution general…

Q: Find a solution for y in terms of x that satisfies the differential equation and passes through the…

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Q: 7. Consider the differential equation y(1-ysin(x))dx + (2x+3ycos(x))dy = 0. a) Find an appropriate…

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Q: ne given differential equation is not exact. sin(x) + 2y cos(x)) dx + 2x cos(x) dy = 0 e given DE is…

A: We have to find the following conditions according to the given information

Q: Find general solutions of the differential equation. If an initial condition is given, find the…

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Q: Linear Differential Equation: dy 1. Solve dx = 1+ 3y tan . 2. Solve ydx – (eY + 2xy – 2x) dy = 0. -

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Q: У(x2 — у2 + 1)dх — x (х2—у2 — 1)dy %3D0 - -

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Q: x2 dx + y(x – 1)dy = 0 %3D

A: The answer is mentioned in below step

Q: Consider the differential equation: (x* cos y) dy + (x+ 3x³ sin y) dx = 0. (a) Show that this…

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Q: If a first order differential equation is expressed as d = f(x,y) O The equation is separable O The…

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Q: . The linear differential equation dx 2 has the integrating factor equal to_ (Note: Simplify or…

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Q: (xy) + 2y] dy 2y ycos (xy)| dx + 2xe2y xcos

A: We have to solve the given differential equation…

Q: A second-order differential equation and its general solution y(x) are given. Determine the…

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Q: ) . Solve the differential equation by using integrating factors. xy' = 6y + x2 y(x) =

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Q: y" + 9y = e cos 3x + x2 + x³e*

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Q: 2. Solve the differential equation given here with boundary conditions using an integrating factor…

A: Solution is given below:

Q: (3 points) To solve the separable differential equation dy + y cos(x) = 6 cos(x), dx we must find…

A: To solve the separable differential equation

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.