Solve the following differential equations:2x dy dx =3y,y(1)=2 - Vidyadip

Question

Solve the following differential equations:$2\text{x}\frac{\text{dy}}{\text{dx}}=3\text{y},\text{y}(1)=2$

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Answer

$2\text{x}\frac{\text{dy}}{\text{dx}}=3\text{y},\text{y}(1)=2$
$\int\frac{2\text{dy}}{\text{y}}=\int\frac{3\text{dx}}{\text{x}}$
$2\log|\text{y}|=3\log|\text{x}|+\log\text{C}$
$\text{y}^2=\text{x}^3\text{C}...(1)$
Put $\text{x}=1,\text{y}=2$
$4=\text{C}$
Put $\text{C}=4$ in equation (1),
$\text{y}^2=4\text{x}^3$

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