Solve the following differential equations:2x dy dx =5y,y(1)=1 - Vidyadip

Question

Solve the following differential equations:$2\text{x}\frac{\text{dy}}{\text{dx}}=5\text{y},\text{y}(1)=1$

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Answer

$2\text{x}\frac{\text{dy}}{\text{dx}}=5\text{y},\text{y}(1)=1$
$\int\frac{2\text{dy}}{\text{y}}=\int\frac{5\text{dx}}{\text{x}}$
$2\log|\text{y}|=5\log|\text{x}|+\text{C}...(1)$
Put $\text{x}=1,\text{y}=1$
$2\log(1)=5\log(1)+\text{C}$
$0=\text{C}$
put $\text{C}=0$ in equation (1),
$2\log|\text{y}|=5\log|\text{x}|$
$\text{y}^2=|\text{x}|^5$
$\text{y}=|\text{x}|^{\frac{5}{2}}$

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