Solve dz/dx-z(2yx+x^2)=x where y =1

i.e dz/dx=2zx+zx^2+x

pls also illustrate the procedure

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- Apr 17th 2011, 07:45 AMsnehalkhairSolve dz/dx-z(2yx+x^2)=x pls help.
Solve dz/dx-z(2yx+x^2)=x where y =1

i.e dz/dx=2zx+zx^2+x

pls also illustrate the procedure - Apr 17th 2011, 09:11 AMtopsquark
This is a first order linear ODE. (At least for y = 1.)

dz/dx - (2x + x^2)z = x

If you can't think of any other way, you can always find an integrating factor. The equation is in the form

z' + P(x)z = Q(x)

so the integrating factor will be of the form:

exp[ (integral) P(x) dx ]

-Dan

Edit: This leaves one heck of an integral to try and solve, though. You might do better to do a series solution...