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) $y=0$ or $y=-\frac3{5x+C}$, away from its pole. (b) $y=\tan\left(\tan^{-1}x+C\right)$, where finite. (c) $y=\frac{Ae^x}{\sqrt{1-A^2e^{2x}}}$, $A\in\mathbb R$, $|A|e^x<1$.

Solving variable separable equations

Solving variable separable equations

Solution:

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