First slide

Types of solutions of differential equations

Question

$The solution of differential equation \frac{d y}{d x} = 1 - x (y - x) - x^{3} (y - x)^{3} is$

Moderate

A

${(y - x)}^{- 2} = c e^{x^{2}} - (1 - x^{2})$
B

${(y + x)}^{- 2} = c e^{x^{2}} - x^{2}$
C

${(y - x)}^{- 2} = c e^{x^{2}} - (1 + x^{2})$
D

$None of these$

Solution

$\begin{array}{l} Put y - x = v \\ \Rightarrow \frac{d v}{d x} + V x = - x^{3} v^{2} \\ v^{- 3} \frac{d v}{d x} + x v^{- 2} = - x^{3} put V^{- 2} = u \\ \Rightarrow \frac{d u}{d x} - 2 x u = 2 x^{3} G.S. is (y - x)^{- 2} = c e^{x^{2}} - (1 + x^{2}) \end{array}$

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