Solve (xy + x)dx = (x² y² + x² + y² + 1)dy. O In(x² + 1) =y² - y + 2 In (y + 1) + c O 1/2 In(x² + 1) = 1/2 y² - y + 2 In (y + 1) + c O 1/2 In(x² + 1) = y² - y + 2 In (y + 1) + c O In(x? + 1) = 1/2 y² - y + 2 In (y + 1) + c

Q: xy' = y + xe/x

A:

Q: y' + xy = xy

A:

Q: Find the general solution of xy'-2y=2x^2lnx, x>0. write the answer explicitly

A:

Q: Solve dy/dx=ax+by+c

A: We need to use substitution method to convert it into separable form

Q: Find the general solution by undetermined coefficients.  y'' + y = 2x2e-x.

A:

Q: Find the solution to the equation y' - y = x2y2

A:

Q: Differentiate. y = Y =_et %3D 3x2 y' = %3D

A: The detailed solution is as follows below:

Q: Q3: Solve the following differential: y" - 4y + 5y = x *******

A:

Q: Solve using the method of undetermined coefficients: y" + 3y" – 10y' = 2 + xe* %3D

A: Given: y''' + 3y'' - 10y' = 2 + xex

Q: Solve: y" - 2y' = xe 4x

A:

Q: x = y+ xe' dx

A:

Q: y' = 2x + 2C₁e2x + 3C₂e³x

A: Formation of Differential Equation: When we seek solution to a differential equation, the general…

Q: Solve: x'y" - 2xy' + 2y =0 2_2)

A: Please refer to the image below

Q: Solve by variation of parameters: 2x²y" +5xy' + y = x² - x

A:

Q: Solve The ODE  y'=2y

A:

Q: Solve (11x + 12)eª dx using Integration by Parts. 11x + 12 and v' = eª. Use u =

A:

Q: y = 2" In (cot (Tx))

A:

Q: Solve by using Homogenous differential equation method: 3- dy Зу dx X +tan() X

A:

Q: Find the solution. y'+ ty = ty3

A:

Q: y' + 3y = 8

A: