Find the general solution of the following differential equations: \(e^{2x^{5}-1}\frac{\mathrm{d}y}{

Question

Find the general solution of the following differential equations: $e^{2x^{5}-1}\frac{\mathrm{d}y}{\mathrm{d}x}=x^{4}$ $\sqrt{1-x^{2}}\frac{\mathrm{d}y}{\mathrm{d}x}=2x-1$ $\frac{\mathrm{d}y}{\mathrm{d}x}=x^{2}+\frac{1}{x^{2}}$

Accepted Answer

$\text{(i)}\ y=-\frac{1}{10}e^{1-2x^5}+C_1$ $\text{(ii)}\ y=-2\sqrt{1-x^2}-\sin^{-1}x+C_2,\ -1<x<1$ $\text{(iii)}\ y=\frac{x^3}{3}-\frac{1}{x}+C_3,\ x\ne0$

Differential Equations - Solving Differential Equations by Direct Integration

Differential Equations - Solving Differential Equations by Direct Integration

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