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Answer to Question #2783 in Differential Equations for Ahmad

Question #2783
solve my differential equation
y'' =(y')3 + x2
Expert's answer
Let’s solve the homogeneous equation:
y''- y'3 = 0
Denote y' as p:
p'p - p3 = 0
dp/dy = p2
p = -1/x + C

Let’s solve nonhomogeneous equitation:
p'p - p3 = 1/p2
p'p3 - p5 = 1
dp/dx = 1/(p (C - p)2) + p2
dx = (p(C - p)2)/(1 + p3(C - p)2) dp

The last equitation hasn’t analytical solution.

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