Solve the differential equation  (dy/dx) + 2y/3 = x / (root of)(y)

Dear Student,
Please find below the solution to the asked query:

We have:dydx+2y3=xyy'+2y3=xy32y'+y=3x2y32y'y+yy=3x232y'y+y32=3x2Let y32=t32y.y'=dtdxdtdx+t=3x2This is first order linear differential equation.Integrating factor=e1.dx=ex, hence we get:dt×ex=32x.ex.dxt×ex=32x.ex.dxt×ex=32x.ex-ddxxex.dxdx Integration by partst×ex=32xex-ex+Ct×ex=32xex-ex+Ct×ex=3ex2x-1+Ct=32x-1+Cexy32=32x-1+Cex

Hope this information will clear your doubts about this topic.

If you have any doubts just ask here on the ask and answer forum and our experts will try to help you out as soon as possible.
Regards

  • 13
What are you looking for?