1. Show that the solution of: dy x? y 1.1 with initial condition , y(1) = 2 dx 1+ x3 is y = V4 + 4x³.

Q: Find the general solution of the equation x(y2 + 1)dx + (1+ x²)dy = 0. A. In(x2 + 1) + 2Arctan y = c…

A: The given equation is; x(y2+1)dx + (1+x2)dy =0

Q: Find the general solution of (x+2y– 4)dx-(2x+5-y)dy=0

A: The given differential equation is of Reducible Homogeneous form . We solve it using following way .

Q: + y²) dx − xy d

A: Here we have;  2(2x2+y2)dx-xydy=0 ............................(1)

Q: (y + 1)dx + (4x – y)dy = 0

A:

Q: Show that the given function y = 5e²x + x is a solution of the IVP 2x subjected to the condition…

A: The given initial value problem dydx-2y=1-2x subject to the condition y0=5 We have to show that…

Q: The solution of (y + x + 5)dy = (y – x + 1) dx is %3D

A: An ordinary differential equation is an equation containing independent variables, dependent…

Q: dy - 2rV1 – y³, -1 < y< 1 dx

A: Given dydx=2x1-y2

Q: 3x²=ay² + (1-4x4) dy = 0 (₁ 2. 1 + x³y² +y + xy = 0

A:

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

A:

Q: x² = 2y²(y-1) y² = 2x²(x+1) x² = 2y²(y+1) y² = 2x²(x-1) dx (3x²-2-²) 4

A:

Q: アT x=2 y=2 7+3x-6y dy dx x0 y=1

A:

Q: 2x dy + y(2 + y²x) dx = 0

A: The given differential equation is

Q: y = V1 -— 2х

A: Our Aim is to differentiate the expression given below:-y=x41-2x

Q: Q2// find the general solution (x³ + 2y³ + x²y)dx – (x³ + 2xy²)dy = 0 %D

A:

Q: (x +Jy?+1) dx x-(y- dy = 0 り*+1

A:

Q: y = elx²+2x+3)2 y = ise dy =? dx

A:

Q: Solve the problem by using Exact DE 3 1. (2 x³ x y² - 2y + 3) dx − (x² y + 2 x) dy = 0

A:

Q: Determine the general solution of (x-2y)dx + (2x+y)dy = 0

A: See the details solution in below

Q: dx xy+3x-y-3 dy xy-2x+4y-8

A:

Q: Determine the solution of 2x (y+1)dx−ydy=0

A: Determine the solution of 2x (y+1)dx−ydy=0

Q: 3. Obtain the general solution of: (x – y)(4x + y) dx + x(5x – y) dy = 0

A: