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Question
Solve the following differential equation.
`y^3 - dy/dx = x dy/dx`
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Solution
`y^3 - dy/dx = x dy/dx`
∴ `y^3 = (1+x) dy/dx`
∴ `dx/((1+x)) = dy/y^3`
Integrating on both sides, we get
`intdx/(1+x )= int dy/y^3`
∴ `log | 1+x| = -1/(2y^2 )+c`
∴ 2y2 log | 1 + x | = – 1 + 2y2c
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