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

**Splint** · September 23rd 2009, 11:14 PM

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

**mr fantastic** · September 23rd 2009, 11:21 PM

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 $\frac{dy}{dx}$ ?

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

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.

**Splint** · September 24th 2009, 01:44 AM

Originally Posted by mr fantastic

Can you get $\frac{dy}{dx}$ ?

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

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

**tanujkush** · September 24th 2009, 01:50 AM

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

**Prove It** · September 24th 2009, 01:55 AM

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

$y = a\sin{bx}$ .

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

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

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

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