3. Solve (2xy – y² + y)dx + (3x² – 4xy + 3x)dy = 0. (Non Exact) 4. Solve the following FOLDE: (2у + x*)dx — хdy %3D 0)

Q: Find the general solution of d²y dy 4- + 4y = 0 - %3D dx?

A: The given differential equation is d2ydx2-4dydx+4y=0.

Q: 5. Solve d²y dy dx² dx +2 + 5y = sin 2x, given that y(0)=3, y'(0)=0.

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Q: 2. x²y² = 3y' +1 dy %3D dx

A: Please refer the attached image for complete solution.

Q: (х + у+4)dx+ (x + у—3)dy %3 0

A: The differential equation M(x,y)dx+N(x,y)dy=0 is said to be exact if there exists a function f(x,y)…

Q: Find the general solution to dy/dx= 6-x^2/2y^3

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Q: Find the general solution of

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Q: I. Find the general solution of the following: 1. dy - 2x²¹ dx y 2. dx = xy dx 3. dy = (6e³x + 1)dx…

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Q: Solve for the general solution of (ylny-e^-(xy))dx+(1/y+xlny)dy=0

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Q: Find the general solution of dx -3 y=2cos3x . dx

A: The given differential equation is. d2ydx2+2dydx-3y =2cos3x This can be written as, D2+2D-3y=2cos3x…

Q: Show that if you differentiate both sides of x2 +2y³ = 6, the result is dy dx 2x + 6y² = 0. Then…

A: Given function is x2+2y3=6 Power rule of differentiation states that  ddxxn=nxn-1 And ddxconstant=0…

Q: Solve dy/dx =( y+x-2) /(y-x-4) Equation s reducible to homogenous form

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Q: б бу-гу2 -14-292 y dx dy

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Q: Q3 (d^2 y)/(dx^2) - 2dy/dx of Undetermined Coefficient) 20e^(-x) cos(x), y(0) = 0 = y'(0) (Use…

A: we have to solve given differential equation by using method of undetermined coefficient

Q: Obtain the particular solution when x = 1 and y = 1 yl? - y² + 1) dn - xlx? - y? - 1) dy = dx – x(x²…

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Q: The solution to (2x – 4y – 3)dy = (x- 2y)dx is:

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Q: Obtain the general solution to the equation. dy 1. y + 2x + 1 dx

A: Given that: dydx=yx+2x+1

Q: What is exact solution for dy/dx =(x2+y2)/(x+y)

A: Given: The given equation is dydx=(x2+y2)x+y

Q: Q.No.3: a) Solve Cauchy-Euler equation d'y 3x3 dx3 d'y + 9x2 + 6x dx2 dy 6y = 1+ x3 dx -

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Q: 5. Find the particular solution (IVP) for the DE below: a) dx +2 =8x when x = 2, y = 6 b) 3y2 = 2x +…

A: Use variable separable method

Q: Solve th D.E using Exact (6x² – y +3)dx+(3y – x – 2)dy

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Q: Solve the particular solution of (xª + y³)dx – 2x° dy= 0 when x = 2, y = 3. -

A: We can rewrite the given equation as,  (xy+y3)dx = 2x3dy xydx+y3dx = 2x3dy

Q: Find the general solution of  dy/dx + y/x= 3/y

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Q: 9. Find the General and Particular solution of = 4y ; y= 3,when x dx

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Q: Solve (1+2.x) dy d²y -6(1+2x)- dy -16y = 8(1 + 2x) with y(0) = 0, y'(0) = 2. dx dx?

A: Given differential equation is: (1+2x)2d2ydx2-6(1+2x)dydx+16y=8(1+2x)2 Given differential equation…

Q: 3 7x + 6x - 5x dy find dx - Example 28. If y = 4

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Q: 30. Find the solution of exe dx-e-2Y dy = 0 %3D

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Q: 4x − 5y + 3)dx − (2x − 3y − 1)dy = 0 how solve this problem?

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Q: 3. Find the General and Particular solution of = 3y ; y= 3,when x = 0 dx

A: Take integration on both side and then put initial value

Q: Find the general solution of the equation: G + 6x) dx + (In x – 2) dy = 0 (x > 0) -

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Q: Solve D.E using Exact from first order (6x² - y+3)dx+(3y² – x- 2)dy

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Q: Find the general solution of 6y2 dx - x (2x3 + y) dy = 0

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Q: (3x + 2y3) dx + 3xy2 dy = 0 ,  y(1) = 1

A: Given: (3x + 2y3) dx + 3xy2 dy = 0 ,  y(1) = 1

Q: Solve the homogenous diff equation of; dy dx x²(y² + 3) y(x³ + 1) 0

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Q: (ve* +y)dx+(2xye* +1)dy = 0

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Q: Find the particular solution of dy - 2y = x³ sin 4x, y(1) = 2. dx %3D -

A: Using method of Linear Differential Equation.

Q: 4. Using homogenous D.E approach, solve (x³ – Зху?)dx %3D (у3 — 3x2у)dy. (v³ – 3x²y)dy. | 2 (ardai…

A: The given differential equation is; (x3-3xy2)dx=(y3-3x2y)dy.

Q: Find an implicit general solution of ( x² + dx + 1+ 4x²y², - y*) dy = 0 %3D 1+4x²y?

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Q: solve the homogenous equation . (2x-3y)dx+(2y-3x)dy=0

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Q: 4(3x+ y – 2)dx – (3x + y)dy = 0

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Q: Solve dy dy + y = 2sin(3x) - dx? dx using the method of undetermined coefficient.

A: We solve the given differential equation by method of undetermined coefficients.

Q: 4. Find 3x 2t dx/e²t dt

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Q: Solve = 1 +y, y(0) = 0 by Picard's method. %3D dx

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Q: Solve the Euler equation d²y dx dy -5y = 0 dx 31 d', 3x2 given that y(1) =1 and y'(1) = 2. intai

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Q: 1. Find the general solution of 3 + = y*(2x*) dx

A: Since you have posted multiple questions in this question which are not interlinked so I have solved…

Q: Find the General and Particular solution of dy/dx = 3y ; y = 3, when x = 0

A: The formula for integration of fractional function is given by: ∫1x=ln|x|. Given: dydx=3y ; y=3 when…

Q: Obtain the general solution to the equation. 3. dx - (у — 2ху)dy

A: Topic - differential Equation

Q: Solve using the integrating factors by inspection and get the general solution of…

A: The given differential equation is, yx2y2+2dx+x(2-2x2y2)dy=0 Now rearrange terms as below:…

Q: 2Y – x²y² -2. dy dx

A: The given differential equation is: dydx=2yx-x2y2

Q: 5) SOLVE dy _ yz %3D x2

A: A differential equation is an equation in x,y and derivatives of y. An ordinary differential…

Q: d) Obtain the particular solution of (2x– 3y+4)dx +3(x-1)dy =0; when x=-1, y = 2

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