# 2nd order inhomgenous eqautions

• Jul 7th 2012, 08:12 PM
Magical
2nd order inhomgenous eqautions
Using the complementary function and particular integral
method, find the solution of the differential equation

a) d^2y/dx^2+3dy/dx+2y=20cos2x
which satifies y(0)=1 and y'(0)=0

b)Briefly

details of this

c) The eqaution d^2y/dx^2+6dy/dx+9y=h(x) has a complementary function y=(ax+b)e^-3x
give detail of the particular integral if h(x) were given by
i)h(x)=5x+6

ii)h(x)=5e^-3x

iii)h(x)=5xe^-3x
• Jul 7th 2012, 08:27 PM
Prove It
Re: 2nd order inhomgenous eqautions
Quote:

Originally Posted by Magical
Using the complementary function and particular integral
method, find the solution of the differential equation

a) d^2y/dx^2+3dy/dx+2y=20cos2x
which satifies y(0)=1 and y'(0)=0

b)Briefly

details of this

c) The eqaution d^2y/dx^2+6dy/dx+9y=h(x) has a complementary function y=(ax+b)e^-3x
give detail of the particular integral if h(x) were given by
i)h(x)=5x+6

ii)h(x)=5e^-3x

iii)h(x)=5xe^-3x

What have you tried?
• Jul 7th 2012, 08:51 PM
Magical
Re: 2nd order inhomgenous eqautions
ive integrated both sides of the eqaution to give dy/dx +3y +y=10sin(2x) and substituted in y=0
to give dy/dx=10sin(2x)
• Jul 7th 2012, 08:57 PM
Prove It
Re: 2nd order inhomgenous eqautions
Quote:

Originally Posted by Magical
ive integrated both sides of the eqaution to give dy/dx +3y +y=10sin(2x) and substituted in y=0
to give dy/dx=10sin(2x)

You can't solve this with direct integration. I suggest you read about Homogeneous and Nonhomogeneous second order ODEs with constant coefficients.