Given that three solutions to the inhomongenous DE equation y''+p(t)y'+q(t)y=g(t)

are y1=1+e^(t^2), y2= 1+te^(t^2), y3= 1+(t+1)e^(t^2),

find the general solution

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- May 21st 2011, 05:28 AMDukeFinding general solution
Given that three solutions to the inhomongenous DE equation y''+p(t)y'+q(t)y=g(t)

are y1=1+e^(t^2), y2= 1+te^(t^2), y3= 1+(t+1)e^(t^2),

find the general solution - May 21st 2011, 11:33 AMJester
Since , and all satisfy the ODE then

and

satisfy

Thus, the general solution is

.

Note that we could have used either for but can adjust the constants such that all we need is . - May 21st 2011, 02:06 PMDuke
Why did you subtract the solutions? Thanks

- May 21st 2011, 07:12 PMJester
It was to get to the homogeneous ODE

If and satisfy your ODE, i.e.

and

then substracting gives

.