- #1

Felipe Lincoln

Gold Member

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- 11

## Homework Statement

Solve the following differential equation such that ##x(0)=1##.

## \dfrac{dx}{dt} + 2tx = 3e^{-t^2}+t##

## Homework Equations

Integrating factor:

##\mu(t) = exp\left(\int_0^t2t \right)##

## The Attempt at a Solution

I used the integrating factor and then got the solution ##x(t) = 3te^{-t^2}+\dfrac{1}{2} + C ## and using the initial condition I got ##x(t) = 3te^{-t^2}+1 ## but if I replace this result into the differential equation I get 2t = t. I first tried to solve it again and got the same solution. Maybe the initial condition should be 1/2 ?