3. Show that the differential equation (1 – 2y + x In a)dx + (e2v – 2x)dy = 0 is exact and find its solutions

Q: solve the differential equation of (x^3 +xy^2-2a^2)dx+(x^2y-y^3-yb^2)dy=0

A: For differential equation ,M dx+N dy=0 is tobe exact if∂M∂y=∂N∂xthen solution is∫M dx+∫ N…

Q: (3) Show that the solution of the differential equation fip + y = -2r"y' is ´d.r r'y"(2r* + c) = 1.

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Q: A particular solution of the differential equation "+3y'+4y = 8x +2 is

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Q: The characteristic equation for the differential equation xy" – 3x²y" + 5xy' + 6y = 0 is :

A: We have to find the characteristic equation of the third order Cauchy-Euler linear homogeneous…

Q: 3. Find all solutions of the given differential equation. dy xy dx x² + 1

A: Given dydx=xyx2+1

Q: The general solution of the differential equation x²y" - 2y = Inx is

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Q: Find the general solution for each of the differential equations given below. Y” + 2y’ + y = e^-1

A: Find the general solution for each of the differential equations given below. Y” + 2y’ + y = e^-1

Q: Find the solution of the differential equation (1+x² )y'+2.xy – 4x²y' = 0 (Bernoulli)

A:

Q: B. Find the general/particular solution of the given higher-order differential equation 5.) dx4 d*y…

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Q: Consider the differential equation: y" – 6y' + 9y = (x + 1)e³* What is the particular solution Yp =…

A: We can solve this using given information. Given y''-6y'+9y=(x+1)e3x What is solution yp? We will…

Q: Find the solution of the differential equation (1+x* )y'+2.xy – 4x°y° = 0 (Bernoulli) %3D

A: We will find out the required general solution .

Q: 2.2 Find the solution of the differential equation d'x dx + + 3z + 8x dt dz %3D dt? dt

A: Given: d2xdt2+dxdt+8x=dzdt+3z

Q: Find the general solution of the first order differential equation dy = 8x +1 and the particular…

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Q: Verify that y = e 3x cos 2x is a solution of the differential equation y"-6y' + 13y = 0

A: To verify that y=e3x cos 2x is a solution of the differential equation y''-6y'+13y=0.

Q: The solution of the exact differential equation (3x² + 4xy)dx + (2x² + 2y)dy = 0 is: None of the…

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Q: 3. Get the general solution of the differential equation (x+2y-4)dx- (2x+y-5)dy%3D0.

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Q: 4. Find the general solution of the differential equation using the method of undetermined…

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Q: Find the solution of the differential equation that satisfies the given initial condition. x In(x) =…

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Q: . The implicit solution for the differential equation y' = x³y is A. In x = y² + c B. 3 lnx = y² + c…

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Q: 2. Find the general solution of the differential equation. Then, use the initial condition to find…

A: Given differential equation y'-4y=6e4x Initial value is y0=0.

Q: 5.- Use the method of undetermined coefficients to find the general solution of the differential…

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Q: | 2. Consider the differential equation y(5) + 3xy4) + 2y = 0 How many linearly independent…

A: **By Bartleby policy I have to solve only first one as these are all unrelated problems**  First…

Q: Find the particular solution of the non-linear ordinary differential equation. y' = -3y + y², y(1) =…

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Q: If xm is a solution of the differential equation x²y" – 2y = 0 then m %3D -

A: Given that a second order differential equation and also given a solution of this equation is xm and…

Q: The solution of the differential equation xy" – 3xy' + 4y = 0 is O ye = Cjx + c2x² O ye = C1x +…

A:

Q: A particular solution of the differential equation y''+3y'+2y=4x+3 is:

A: Solving the differential equation

Q: (a) Find the general solution of the differential equation d²y dx² +9y = x² + x + 1.

A:

Q: Solve the Euler-Cauchy differential equation d²y dy 3x- +4y = In2x- Inx %3D dx

A: Given: Let us assume, x2d2ydx2-3xdydx+4y=ln2(x)-ln(x)......(1)

Q: The solution of the exact differential equation (3x² + 4xy)dx + (2x² + 2y)dy = 0 is: None of the…

A:

Q: ƏM aN 6. In the differential equation (y² –x² - 4x-1dy+2y(x+y+2)dx = 0, what is

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Q: (군2-1) 을 + 2y3 (+ 1)°

A: Given ODE : (x2-1)dydx+2y=(x+1)2 ⇒dydx+2yx2-1=(x+1)2x2-1⇒dydx+2yx2-1=x+1x-1 Which Linear…

Q: 5. Find the solution of the differential equation 2dy + ydx = y'(x-1)dx (Bernoulli)

A: given that

Q: If yy of a differential equation is ce2x + Cze3x + cze-3x, then W = (a) 0 (b) (c) 5e-* (d) e5x d O a…

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Q: Solve the differential equation of  dy/dx - b2y = c1eb1x; where c1, b1, and b2 are constants and b1…

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Q: If yH of a differential equation is cje2* + cze3x + cze-3x, then W1 = %3D (a) 0 (b) 9 (c) 5e-* (d)…

A: If yH of a differential equation is c1e2x+c2e3x+c3e-3x, then we have to find the Wronskain W.

Q: (5) Find the general solution for the differential equation (x² – 2xy – y²)dx – (x + y)²dy = 0.

A: It is a first order non linear ordinary differential equations and also it is a exact equation…

Q: The solution of a certain differential equation is of the form y(t) = aexp(2t) +bexp(4t), %3D hore a…

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Q: Find general solutions of the differential equation     x^2y'+2xy=5y^3

A: Given Data The differential equation is x²y'+2xy=5y3.   Divide the differential equation by y3 and…

Q: 4) Find the general solution of the differential equation xy" – (2x + 1)y + (x + 1)y = (x² +x –…

A:

Q: 1. Find the general solution of the given differential equation using MUC: y(4) – 4y(3) – 21y(2) +…

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Q: 3. Consider the differential equation a²y" – x(x + 2)y + (x + 2)y = 0, x > 0 %3D a) Show that yı(x)…

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Q: 11. Find the general solution of the first-order linear differential equation. x'y'+2y a. 2x2 b. 2x2…

A: To find the general solution of the following differential equation.  x3y' +2y = e1/x^2

Q: 2. Find the solution of the differential equation ₂ dy 2x² = dx 3xy + y². which satisfy an initial…

A: Solved below.

Q: 5. Find the general solution of the given differential equation y" + 3y" + 3y + y = 0

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Q: The solution of the differential equation (x³ + 3xy²)dx+ (y³ + 3x?y)dy= 0 is

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Q: b) Write down a linear, homogenenous 2nd order differential equation with constant coefficients that…

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Q: 3. Find the general solution of the differential equation y" + 4y = 2 + e²" cos 2x

A: Given differential equation is 2nd order differential equation. General solution= Complementary…

Q: Verify that y = e3x cos 2x is a solution of the differential equation y"-6y +13y = 0.

A: We have to show that y is the solution of given differential equation

Q: The general solution for the differential equation2 x²3"+3xy'+y= 0 is O y=c,x+c,x!nx

A: