Thread: 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
explain how you could check whether your answer is

correct. If you would use technology to help you check, give
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

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
explain how you could check whether your answer is

correct. If you would use technology to help you check, give
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?

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)

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.