# differential equation

• Mar 22nd 2009, 09:51 AM
coliechrist5
differential equation
some one please help me ive been trying to do this homework forever and i just dont know how. i have a few questions so as many that you could answer would be very helpful.

verify the solution to the differential equation: y'' + y' + 2y=sinx, where y(x)=0.1sinx-0.3cosx.

For the following questions you just need to gie a particular solution.

y''' = sin(2x), y(0)=4, y'(0)=10, y''(0)= -8 ?

square root of x * y' = 2(x^2)y - 5xy - 7y ?

(10x^2 + 7x) / 2xy = y*y' ?

(x^2)y^1 +(2x^3)y = 8x ?

and lastly 2y'' +5y' - 6y = 0

if someone could help me that be great thank you so much
• Mar 22nd 2009, 11:24 AM
CaptainBlack
Quote:

Originally Posted by coliechrist5
verify the solution to the differential equation: y'' + y' + 2y=sinx, where y(x)=0.1sinx-0.3cosx.

Differentiate $y(x)=0.1 \sin(x)-0.3 \cos(x)$ twice and then substitute $y$, $y'$ and $y''$ into the left hand side of the DE simplify and show that you are left with $\sin(x)$.

CB