Find the particular solution of the following differential equations: \(\frac{y}{x} \frac{\mathrm{d}

Question

Find the particular solution of the following differential equations: $\frac{y}{x} \frac{\mathrm{d}y}{\mathrm{d}x} = \frac{y^2 + 1}{x^2 + 1}$; $y = 0$ when $x = 1$ $e^t \frac{\mathrm{d}s}{\mathrm{d}t} = \sqrt{s}$; $s = 4$ when $t = 0$ $x^2 \frac{\mathrm{d}y}{\mathrm{d}x} + 1 + y^2 = 0$; $y = 1$ when $x = \frac{4}{\pi}$ $(1 + \cos 2x) \frac{\mathrm{d}y}{\mathrm{d}x} = y \sin 2x$; $y = 2$ when $x = \frac{\pi}{4}$

Accepted Answer

(a) $2y^2 = x^2 - 1$ ; (b) $2\sqrt{s} = -\frac{1}{e^t} + 5$ ; (c) $y = \tan \frac{1}{x}$ ; (d) $y = \frac{2}{\sqrt{1 + \cos 2x}}$.

Differential Equations - Differential Equations - General

Differential Equations - Differential Equations - General