First slide

Methods of solving first order first degree differential equations

Question

The differential equation of the family of parabolas with vertex at (0,-1) and having axis along the y-axis is

Moderate

A

${xy}^{1} + y + 1 = 0$
B

${xy}^{1} - 2 y-2 = 0$
C

${xy}^{1} - y-1 = 0$
D

${yy}^{1} + 2 xy+1 = 0$

Solution

$\begin{array}{l} x^{2} = 4 a (y + 1) - c . . . . . . . . . . . . . . (i) \\ \Rightarrow 2 x = 4 a \frac{dy}{dx} \Rightarrow 4 a = \frac{2 x}{y^{1}} . . . . . . . . . . . . . (i i) \\ From 1 and 2 \Rightarrow {xy}^{1} - 2 y - 2 = 0 \end{array}$

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