# Thread: d^2y/dx^2 + b^2y=0 Show y=asinbx is a solution.

1. ## d^2y/dx^2 + b^2y=0 Show y=asinbx is a solution.

Hi,

I have encountered this problem and don't know how to work it out. Anyone willing to explain it to me?

An analysis of the motion of a particle resulted in the differential equation d^2y/dx^2 + b^2y=0

Show that y=asinbx is a solution to the equation.

Thanks
David

2. Originally Posted by Splint
Hi,

I have encountered this problem and don't know how to work it out. Anyone willing to explain it to me?

An analysis of the motion of a particle resulted in the differential equation d^2y/dx^2 + b^2y=0

Show that y=asinbx is a solution to the equation.

Thanks
David
Can you get $\displaystyle \frac{dy}{dx}$?

$\displaystyle \frac{d^2y}{dx^2}$?

Can you substitute the appropriate expressions into the differential equation?

Can you simplify after substituting?

You need to show your work and say where you get stuck.

3. Originally Posted by mr fantastic
Can you get $\displaystyle \frac{dy}{dx}$?

$\displaystyle \frac{d^2y}{dx^2}$?

Can you substitute the appropriate expressions into the differential equation?

Can you simplify after substituting?

You need to show your work and say where you get stuck.
Thanks for your reply Mr Fantastic. This equation is a bit more complex than anything I have done so far. I could try and attempt it but I would really only be making educated guesses. Would you be able to step me through it and explain the steps as you go?

Thanks
Splint

OK, I'll give it a try but I think I'm destined to fail.....And sorry for not using Latex, I'm still learning...

If the second derivitive is -b^2y then the derivitive may be -b^3y^2/6? and the function may be -b^4y^3/72?

If -b^4y^3/72 then I cannot see how y=asinbx can be a solution.

That's where I'm at.
Thanks
David

4. Originally Posted by Splint
Hi,

I have encountered this problem and don't know how to work it out. Anyone willing to explain it to me?

An analysis of the motion of a particle resulted in the differential equation d^2y/dx^2 + b^2y=0

Show that y=asinbx is a solution to the equation.

Thanks
David

You need to look up the derivation of any Simple Harmonic Motion.

For starters check this out

5. Originally Posted by Splint
Hi,

I have encountered this problem and don't know how to work it out. Anyone willing to explain it to me?

An analysis of the motion of a particle resulted in the differential equation d^2y/dx^2 + b^2y=0

Show that y=asinbx is a solution to the equation.

Thanks
David
Note that you are not asked to FIND a solution, you are just asked to VERIFY a solution.

The solution you are told to verify is

$\displaystyle y = a\sin{bx}$.

So $\displaystyle \frac{dy}{dx} = ab\cos{bx}$

and $\displaystyle \frac{d^2y}{dx^2} = -ab^2\sin{bx}$.

What does $\displaystyle \frac{d^2y}{dx^2} + b^2y$ equal?