Question 1: Use separation of variable method

a) ^dy_/dx= x , b) ^dy_/dx= ^y_/x

_{Question 2}

_Given ^dy_/dx= ^y_/x with initial value y(0)=0, find the solution of the initial value problem

Question 3

Solve ^dy_/dx - 2y(x+1)=0 with y(0)=1. Find the solution

Question 4

_Given ^dy_/dx =2x + 5 with initial condition y(0)=1, find the solution of the initial value problem

Question 5

Solve ^dy_/dx = ysinx with initial condition y(0)=1. Find the solution to initial value problem.

Question 6

Solve Homogeneous equation

a) 2X^2dy_/dx= X² + y ²

b) (X² + xy) ^dy/_dx=xy - y²

Question 7

Solve Distinct real roots

a) y^II - y^I - 2y =0, y(0)=2 , y^I(0)=7

b) y^II + 4y^I - 5y =0

c) 6y^II + y^I - y =0

d) y^II + 2y^I - 4y =0, y(0)=6 , y^I(0)=-6

Question 8

Solve repeated real roots

a) y^II 9y^I + 8y =0

b) y^II - 6y^I + 8y =0

c) 9y^II + y =0, y^II(0)=2 , y^I (0)=2

d) y^II + 6y^I + 34y =0, y(10)=5 , y^I (10)=-5

e) y^II + 2y +y =0, y(0)=1 , y^I (0)=1

d) y^II - y^I + 0.25y =0, y(0)=2 , y^I (0)=

Question 9

Solve Complex conjugate roots

a) y^II - 6y^I + 25y =0

b) y^II - 6y^I + 8y =0

c) y^II + 9y^I + 14y =0 , y(5)=4 , y^I (5)=2

d) 9y^II + y =0 , y(0)=-2 , y^I (0)=2

e) 3y^II - 2y^I +y =0

f) y^II + y +y =0 , y(0)=1 , y^I (0)=1