What is the differential equation for dydx=xey-2x?
Solution.
The differential equation is
dydx=xey-2x⇒dydx=xeye-2x⇒dyey=xe-2xdx
Integrating both sides
∫dyey=∫xe-2xdx⇒∫e-ydy=∫xe-2xdx⇒-e-y=x-12e-2x-∫1-12e-2xdx⇒-e-y=-12xe-2x-14e-2x+c∴e-y=-12xe-2xx+12+c
Hence, the solution to the given differential equation is e-y=-12xe-2xx+12+c.
For the given differential equation find the general solution. xdydx+2y=x2logx