Verifying...Diff EQ

[Daniel_Feldman]

I need to verify that

Q(t)=[E/(R(y^2+(120pi)^2))][120pi(e^(-yt)-cos(120pi*t))+ysin(120pi*t)]

satisfies the initial value problem

dQ/dt=-Q/RC+(E/R)sin(120pi*t), Q(0)=0.

The constant y=1/(RC) has units of hertz.

Is there any way to do this besides using integration by parts twice? I can take the derivative of Q(t) but that looks pretty complicated too...

 

[tkhunny]

"Verify" usually suggests the solution is already given and you have only to demonstrate it. It sounds like you are trying to SOLVE the differential equation.

 

[Deleted member 4993]

I need to verify that

Q(t)=[E/(R(y^2+(120pi)^2))][120pi(e^(-yt)-cos(120pi*t))+ysin(120pi*t)]

satisfies the initial value problem

dQ/dt=-Q/RC+(E/R)sin(120pi*t), Q(0)=0.

The constant y=1/(RC) has units of hertz.

Is there any way to do this besides using integration by parts twice? I can take the derivative of Q(t) but that looks pretty complicated too...

That is what you got to do...