Solve the following differential equation 5 dy dx =e^xy^4 - Vidyadip

Question

Solve the following differential equation
$5\frac{\text{dy}}{\text{dx}}=\text{e}^\text{x}\text{y}^4$

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Answer

We have $5\frac{\text{dy}}{\text{dx}}=\text{e}^\text{x}\text{y}^4$ $\Rightarrow\frac{5}{\text{y}^4}\text{dy}=\text{e}^\text{x dx}$Integrating both sides, we get
$\int\frac{5}{\text{y}^4}\ \text{dy}=\int\text{e}^\text{x}\text{dx}$ $\Rightarrow\frac{-5}{3\text{y}^3}=\text{e}^\text{x}+\text{C}$ Hence, $\frac{-5}{3\text{y}^3}=\text{e}^\text{x}+\text{C}$ is the required solution.

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