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

Question

Find the general solution of the following differential equations. $\frac{\mathrm{d}y}{\mathrm{d}x} = 3x^2 - 4$ $\frac{1}{x} \frac{\mathrm{d}y}{\mathrm{d}x} = \frac{1}{x^2 + 1}$

Accepted Answer

(a) $y=x^{3}-4x+C$ ; (b) $y=\frac{1}{2}\ln(x^{2}+1)+C$.

Example of direct integration solution

Example of direct integration solution