Solve the following differential equation ( dy dx )=K;y(0)=1 - Vidyadip

Question

Solve the following differential equation
$\sin\Big(\frac{\text{dy}}{\text{dx}}\Big)=\text{K};\text{y}(0)=1$

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Answer

$\sin\Big(\frac{\text{dy}}{\text{dx}}\Big)=\text{K};\text{y}(0)=1$
$\frac{\text{dy}}{\text{dx}}=\sin^{-1}\text{K}$
$\text{dy}=\sin^{-1}\text{k dx}$
$\int\text{dy}=\int\sin^{-1}\text{K dx}$
$\text{y}=\text{x}\sin^{-1}\text{K}+\text{C}$
Put x = 0, y = 1
1 = 0 + C
1 = C
Put C = 1 in equation (1),
$\text{y}=\text{x}\sin^{-1}\text{K}+1$
$\text{y}-1=\text{x}\sin^{-1}\text{k}$

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