# Homework Help: Finding particular solution to differential equations

1. Oct 16, 2012

### lillybeans

There are two questions that I am trying to solve on web assignment. The goal is to find a general form of a particular solution to each ODE. The question asks me to represent all constants in the solution using "P,Q,R,S,T..etc.", in that order.

1. y'''-9y''+14y'=x2
2. y''-9y'+14y=x2e4x

For the first one I wrote:
yp=Px3+Qx2+Rx

Second one:
yp=(Px2+Qx+R)e4x

Neither of the answers are correct, according to the computer. Where did I go wrong?

Thanks.

2. Oct 16, 2012

### Zondrina

The answers are not correct because you're not solving the equations correctly.... First do you understand that your equations are non-homogenous?

3. Oct 16, 2012

### lillybeans

Yes, of course, that's why I am asked to find a particular solution. Where did I go wrong? please let me know!

4. Oct 16, 2012

### Zondrina

Okay, so take for example your second question. Notice that your derivatives and original function have to add up to x2e4x?

So your general solution must have the form : y = A(x2e4x) where A is some constant number.

Now take the required derivatives and see if they satisfy your equation. ( You'll get a bunch of constants which you have to add together and solve for A for the particular solution you want ).

5. Oct 16, 2012

### lillybeans

I don't quite understand why your guess for the particular solution has the form Ax2e4x as opposed to (Ax2+Bx+C)e4x. Shouldn't you use the general form of the second degree polynomial?

6. Oct 16, 2012

### Zondrina

A non-homogenous equation with constant coefficients has the general solution y = Ag(t) where A is a constant.

7. Oct 16, 2012

### lillybeans

Then suppose for y''-9y'+14y my yp=Ax2e4x

Then

y'=2Axe4x+4Ax2e4x
y''=2Ae4x+8Axe4x+8Axe4x+16Ax2e4x

When you plug this all back into the original equation, equate the coefficients to solve for A, it doesn't work. Need more than just one constant.