First slide

Methods of solving first order first degree differential equations

Question

$Solution of the differential equation (1 + y + x^{2} y) d x + (x + x^{3}) d y = 0 is$

Moderate

A

$x y = - \tan^{- 1} x + c$
B

$x^{2} y = - \tan^{- x} + c$
C

$x y^{2} = \tan^{- 1} x + c$
D

$x y^{2} = \cot^{- 1} x + c$

Solution

$\begin{array}{l} 1 + y (1 + x^{2}) + x (1 + x^{2}) \frac{d y}{d x} = 0 \\ \frac{d y}{d x} + \frac{1}{x} y = \frac{- 1}{x (1 + x^{2})} I . F = \int \frac{1}{x} d x = x . \\ Sol.is y \cdot x = \int x {(\frac{- 1}{x (1 + x^{2})})}^{d x} = - \tan^{- 1} x + c \end{array}$

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