Struggling with a Nonlinear Nonhomogenous ODE?

[DreDD]

Homework Statement

y' + y = t^2 , y(0) = 6, y'(0)= -6

Homework Equations

The Attempt at a Solution

first i tried to separate variables using y = ux but can't forward on and then i tried undetermined coeff. method. i found homogenous and particular solution but i am not sure about the solution because there is no need to use y'(0)=-6 and i really don't sure can i use this method for the first order ode.

 

[gabbagabbahey]

If you show me your homogeneous and particular solutions, I'll stand a better chance of telling you what is wrong with them than if I just wildly guess at what you may have done wrong! ;0)

 

[DreDD]

x+1 = 0
x = -1

Yh = c1 e^-x

Yp= K2 x^2 + K1x + K0 and take Yp' and write the Yp and Yp' to the eq'n find K2, K1 and K0

Yp = x^2 - 2x +2

Y = c1 e^-x + x^2 - 2x + 2

there is only c1 and i don't need the second initial value

 

[gabbagabbahey]

Shouldn't your y's be functions of t instead of x?!

and since y'(t)+y(t)=t^2, y'(0)+y(0)=0 => y'(0)=-y(0) which is consistent with your initial values, and so you can use either of them to find c1.

If on the other hand, you were given y(0)=6 and y'(0)=3, then there would be no solution since these initial conditions are inconsistent with your ODE.

Luckily, your initial conditions are consistent and so your method and solution are correct!

 

[DreDD]

thanks for the help yes u r right it should be t . i don't like t :D

 

[tiny-tim]

thanks for the help yes u r right it should be t . i don't like t :D

t is good for you! ​

welcome to PF!

 

[DreDD]

t is good for you! ​

welcome to PF!

thx :D but it confuses my mind :D

by the way any other ways to solve this eq'n?

 

[gabbagabbahey]

try "t" with ginseng...that should help your mind out

...as for other methods, I'm sure there are a few (such as power series solutions) but aside from plugging it into mathematica; this is the easiest way I know of.