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First Order Differential Equations (Integrating factor) help

a) a differential equation is given by x(d^2 y/dx^2) - dy/dx = 3x^2, show that the substitution u = dy/dx transforms this differential equation into du/dx - u/x = 3x.
b) By using an integrating factor, find the general solution of du/dx - u/x = 3x. Give your answer in the form u = f(x).
c) Hence find the general solution of the differential equation x(d^2 y/dx^2) - dy/dx = 3x^2.
I've done part a and b (for b I got u = 3x^2 + cx). But how do I do part c using that?
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Original post by TAEuler
a) a differential equation is given by x(d^2 y/dx^2) - dy/dx = 3x^2, show that the substitution u = dy/dx transforms this differential equation into du/dx - u/x = 3x.
b) By using an integrating factor, find the general solution of du/dx - u/x = 3x. Give your answer in the form u = f(x).
c) Hence find the general solution of the differential equation x(d^2 y/dx^2) - dy/dx = 3x^2.
I've done part a and b (for b I got u = 3x^2 + cx). But how do I do part c using that?


y = integral u dx

Edit: don't forget the integration constant.
(edited 5 years ago)

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