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) $y=\frac12\ln(x^2+1)+C$, on an interval with $x\ne0$.

Example of direct integration solution

Example of direct integration solution

Solution:

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