Solve the following differential equations. $y \frac{\mathrm{d}y}{\mathrm{d}x} = \sin x$ \(\frac{1

Question

Solve the following differential equations. $y \frac{\mathrm{d}y}{\mathrm{d}x} = \sin x$ $\frac{1}{x} \frac{\mathrm{d}y}{\mathrm{d}x} = \frac{1}{x^2 + 1}$ $\frac{y^2}{x^3} \frac{\mathrm{d}y}{\mathrm{d}x} = \ln x$ $e^x \frac{\mathrm{d}y}{\mathrm{d}x} = \frac{x}{y}$ $v^2 \frac{\mathrm{d}v}{\mathrm{d}t} = (2 + t)^3$ $\tan x \frac{\mathrm{d}y}{\mathrm{d}x} = 2y^2 \sec^2 x$

Accepted Answer

(a) $\frac{1}{2} y^2 = -\cos x + c$ ; (b) $y = \frac{1}{2} \ln(x^2 + 1) + c$ ; (c) $\frac{1}{3} y^3 = \frac{1}{4} x^4 \ln x - \frac{1}{16} x^4 + c$ ; (d) $\frac{1}{2} y^2 = -xe^{-x} - e^{-x} + c$ ; (e) $\frac{1}{3} v^3 = \frac{1}{4}(2 + t)^4 + c$ ; (f) $-\frac{1}{2y} = \ln|\tan x| + c$

Differential Equations - Method of Separable Variables

Differential Equations - Method of Separable Variables