Find the general solution of the following differential equations. \(3 \frac{\mathrm{d}y}{\mathrm{d}

Question

Find the general solution of the following differential equations. $3 \frac{\mathrm{d}y}{\mathrm{d}x} = 5y^2$ $(1 + x^2) \frac{\mathrm{d}y}{\mathrm{d}x} = 1 + y^2$ $\frac{\mathrm{d}y}{\mathrm{d}x} - y(1 + y^2) = 0$

Accepted Answer

(a) $\frac{1}{y} = -\frac{5}{3}(x+c)$ ; (b) $y = \tan(\arctan x + c)$ ; (c) $\frac{y^2}{1+y^2} = Ae^{2x}$.

Solving variable separable equations

Solving variable separable equations