# Math Help - Strange Differental Equation Pls Help

1. ## Strange Differental Equation Pls Help

Please help to solve the nonhomogenious side of this differential equation.

so the equation is y"+4y'+4y=25*sinX

can't solve the equation after putting back of the first and the second derive of the probe function.

And the probe function is: y=A*sinX+B*cosX+C
First derive: y'=A*cosX-B*sinX
Second derive: y"=-A*sinX-B*cosX

If you put it back its gonna be a huge mess

Pls Help

2. Originally Posted by gergofoto
Please help to solve the nonhomogenious side of this differential equation.

so the equation is y"+4y'+4y=25*sinX

can't solve the equation after putting back of the first and the second derive of the probe function.

And the probe function is: y=A*sinX+B*cosX+C
First derive: y'=A*cosX-B*sinX
Second derive: y"=-A*sinX-B*cosX

If you put it back its gonna be a huge mess

Pls Help
Plugging in:

$-A \sin{x} - B \cos{x} + 4 A \cos{x} - 4 B \sin{x} + 4 A \sin{x} + 4 B \cos{x} = 25 \sin{x}$

$(3A - 4B) \sin{x} + (4A + 3B) \cos{x} = 25 \sin{x}$

Now just compare coefficients.