Solve the following differential equation dy dx = ^2y - Vidyadip

Question

Solve the following differential equation
$\frac{\text{dy}}{\text{dx}}=\sin^2\text{y}$

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Answer

We have $\frac{\text{dy}}{\text{dx}}=\sin^2\text{y}$ $\Rightarrow\text{dx}=\frac{1}{\sin^2\text{y}}$ $\Rightarrow\text{dx}=\text{cosec}^2\text{y dy}$ Integrating both sides, we get $\int\text{dx}=\text{cosec}^2\text{y dy}$ $\Rightarrow\text{x}=-\cot\text{y}+\text{C}$$\Rightarrow\text{x}+\cot\text{y}=\text{C}$
Hence, $\Rightarrow\text{x}+\cot\text{y}=\text{C}$ is the required solution.

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