Question

solve th following differential equation
dr/dt=(t+r)/t

Answer 1

\[\frac{dr}{dt}=\frac{(t+r)}{t}\]\[\frac{dr}{dt}=1+\frac{r}{t}\]\[\frac{dr}{dt}-\frac{r}{t}=1\]First order linear DE, use integrating factor to solve it.

Answer 2

\[y' + p(x)y = q(x)\]\[\alpha = exp[\int p(x) dx]\]\[y=\frac{1}{\alpha}\int\alpha\times q(x)dx\]