Carol Valentine

2022-01-20

How to solve ${x}^{\prime }\left(t\right)=\frac{x+t}{2t-x}$?

Maria Lopez

Expert

Your differential equation is homogenous of order one. You did it right finding $\frac{dy}{dt}=\frac{f\left(y\right)-y}{t}$. So you can integrate of both sides in last equation till your solution is achieved respect to y(t) and t. Then you can substitute $x\left(t\right)=y\left(t\right)t$ in your solution and then apply the initial condition.