Differential Equations Answers

(D^2-2D+3)y=X^2-1

find the differential equation:

2x + 6 y y' =(x^2+3y^2/y)y'

Determine the Integrating factor and identify the solution of general/initial value problem

a) (𝑥2 +1)𝑦′ +2𝑥𝑦=4𝑥2 ; 𝑦(0)=0

1+𝑥2

b)𝑦′+ 𝑦 =3𝑥2 𝑥𝑙𝑛𝑥 ln 𝑥

c) (𝑥2 + 1) 𝑦′ + 4𝑥𝑦 = 𝑥 ; 𝑦(2) = 1

Identify the type of equations and Solve

a) 𝑦′ = 𝑥𝑦 1+𝑥2

b) sin 𝑦 𝑑𝑥 + cos 𝑦 𝑑𝑦 = 0

c) 𝑑𝑦 = 2𝑡 (𝑦2 + 9 )𝑑𝑡

Show that the functions defined below is solution of the Differential Equations or not

a)𝑦=𝑥+3𝑒−𝑥, 𝑦′+𝑦=𝑥+1,𝑤h𝑒𝑟𝑒 𝑦′=𝑑𝑦 𝑑𝑥

b)𝑦=2𝑥2 +𝑒𝑥 +6𝑥+7, 𝑦′′ −3𝑦′ +2𝑦=4𝑥2 c)𝑦= 1 , (1+𝑥2)𝑦′′+4𝑥𝑦′+2𝑦=0

d) 𝑢 = 𝑒3𝑥 cos 2𝑦 , 𝑢𝑥𝑥 − 2 𝑢𝑦𝑦 = 17 𝑢 , 𝑢𝑥𝑥 = 𝑑2𝑢 𝑑𝑥2

Solve the initial-value problem

1. y" - 3y' - 10y = 0, y(0) = 0, y'(0) = 7.

2. y"+14y' + 50y = 0,y(0) = 2, y'(0) = -17

3. 6y"-y'-y = 0, y(0) = 10, y'(0) = 0

4. 6y"+y'-y = 0, y(0) = -1, y'(0) = 3

(D²-2DD'+D'²)z=cosy-xsiny

Using the Frobenius method, solve the following ODE:

x²y"+4xy'+(x²+2)y=0

Solve (D^2 -4D+3)y = e^x cos 2x + cos3x 

Given dy/dx=y²/25 and y = 5 when x = 0 Find x when y =2