Solve the initial value problem. 2x* - х - 4 2 dy X dx (x+1)(у+1) y(1) = 3

Q: (a)((x+1)² – y²)ª– (2(x+1)y – 10(x+1)²) = 0 dx

A:

Q: Solve: x'y" - 7xy' + 41y =0

A:

Q: y (3x² √ + 1 ) dx = (-) dy solve exact equation

A: Step 1: Step 2: Step 3: Step 4:

Q: 5. (1+2xVx2 - y² )dx-(2yVx2-y? )dy =0

A:

Q: The general solution of y' x2 can be written in the form

A:

Q: dy ax + hy +g 4. = 0. dx hx + by + f

A:

Q: 3x+4x+1 6. J x-x+4x-4

A: Indefinite integration

Q: 1. Solve the equation y2 + 6x = y(3y – 2x)y'

A:

Q: (2x2y+3y3)dx - (x3+2xy2)dy = C Solve for Particular Solution when x = 1, y = 1

A:

Q: -x-1)dx= -e-2 А. 2e е-2 В. C e+2 2e Зе- 2 D. 2e 2e

A:

Q: 2. S (2x-5)dx x2-5x+3

A:

Q: 1. Write the equation in the standard form. (2) (1-2x-x²)+2(1+x)y'-2y=0

A: The standard form of the second order differential equation is: y''+P(x)y'+Q(x)y=f(x)

Q: Solve the following edo y²dx + (x² + xy + y²)dy = 0, y(0) = 1

A:

Q: dy Q.2 Solve x/1+ y² + yv1 +x² = 0. dx

A: The expression is x1+y2+y1+x2dydx=0 Multiply both sides by 11+x2·1+y2…

Q: dy x+y+1 5. dx 2x + 2y+3

A:

Q: 7. (x+2yXdx- dy) = dx + dy. %3D

A:

Q: - 4. 3y(x² − 1)dx + (x³ + 8y − 3x)dy = 0; when x = 0, y = 1

A:

Q: Find the solution. (dy/dx) + xy = xy³ A x = (ce-²-1) By = (ce²+1) 7² y = (ce x²-1) x = (ce)² + 1) ²…

A: We have given a differential equation ,  dydx + xy = xy3 Multiply throughout by dx ,  dy + xy dx =…

Q: Solve the IVP by substitution. (3x2 - 2y2)y' = 2xy;  y(0) = -1

A: Substitute  x = vy and than solve using method of separation of variables.

Q: 1.² T 20 40x-x² 9√x²+y2 dydx=

A: We have to solve ∫020∫x40-x29x2+y2dydxThe region bounded by0≤x≤20x≤y≤40x-x2⇒x=y and y=40x-x2squaring…

Q: Solve the initial value problem. O A. dy dx Begin by separating the variables. Choose the correct…

A:

Q: 4 Solve for y(x) y"-y-16=0

A:

Q: ii) Solve (x D²– 3xD+4) y = x² given that y(1) =1 and %3D - y'(1)= 0.

A:

Q: Solve step by step in digital format 4.-(4- y²) dx - (4x²)dy = 0 Solve step by step in digital…

A: