dx/dt - 5x = -3Ae^2t
---->
2x-5x^2 = -3Ae^2t
what should i do to get the answer?
thx
First this is a linear constant coefficeient non-homogeneous ODE. So the general solution is the sum of the general solution of the homogeneous problem:
$\displaystyle \frac{dx}{dt} - 5x = 0\ \ \ \ \ (1)$
and a particular integral of:
$\displaystyle
\frac{dx}{dt} - 5x = -3Ae^{2t}\ \ \ \ \ (2)
$
You should know how to find the general solution to $\displaystyle (1) $, and to find a particular integral of $\displaystyle (2)$ try a solution of the form:
$\displaystyle
x(t)=k e^{2t}
$
CB