First slide

Methods of solving first order first degree differential equations

Question

$The solution of the differential equation \frac{d y}{d x} = \frac{x - 2 y + 1}{2 x - 4 y} is$

Moderate

A

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

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

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

$x - 2 y + x^{2} = c$

Solution

$\begin{array}{l} \frac{d y}{d x} = \frac{x - 2 y + 1}{2 (x - 2 y)} \\ Put u = x - 2 y \cdot \frac{d u}{d x} = 1 - 2 \frac{d y}{d x} \end{array}$

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