Solve the differential equations: $x\frac{\mathrm{d}y}{\mathrm{d}x}=xy+y$ when $y=2$, $x=3$ \(

Question

Solve the differential equations: $x\frac{\mathrm{d}y}{\mathrm{d}x}=xy+y$ when $y=2$, $x=3$ $\frac{\mathrm{d}y}{\mathrm{d}x}+y\sin x=0$ when $y=2$, $x=0$ $\frac{\mathrm{d}y}{\mathrm{d}x}=\frac{y-1}{x(x+1)}$ when $y=2$, $x=1$

Accepted Answer

$\text{(i)}\ y=\frac{2}{3}xe^{x-3},\ x>0$ $\text{(ii)}\ y=2e^{\cos x-1},\ x\in\mathbb{R}$ $\text{(iii)}\ y=\frac{3x+1}{x+1},\ x>0$

Differential Equations - Solving Differential Equations by Separation of Variables

Differential Equations - Solving Differential Equations by Separation of Variables

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