Question

Is the diff equation linear? Separable? Both? Neither?

X dx/dt + t^2 x = sin t


I have it to be separable but not linear??

Answer 1

\[x \frac{\text dx}{\text dt} + t^2 x = \sin t\]
\[\frac{\text dx}{\text dt} + t^2 = \frac{\sin t}x\]
\[\frac{\text dx}{\text dt} = \frac{\sin t}x-t^2\]

Answer 2

how did you separate the variables?