Question

Differential Equations Problem

Answer 1

Answer:

$y=\frac{t^2e^{2t}}{3}+ce^{2t}$

Step-by-step explanation:

We have given differential equation $\frac{dy}{dt}-2y=t^2e^{2t}$

We know that linear differential equation is given by $\frac{dy}{dt}+Py=Q$

On comparing with standard equation P = -2 and Q= $t^2e^{2t}$

Now integrating factor $IF=e^{-Pdt}$

$IF=e^{-2dt}=e^{-2t}$

Now solution of differential equation is given by

$y\times IF=\int\ IF\times Q\ dt$

$y\times e^{-2t}=\int\ e^{-2t}\times t^2e^{2t}\ dt$

$y\times e^{-2t}=\frac{t^2}{3}+c$

$y=\frac{t^2e^{2t}}{3}+ce^{2t}$