The particular solution of the differential equation \(\frac{d y}{d x}=\sec y, y(0)=0\) is
The particular solution of the differential equation \(\frac{d y}{d x}=\sec y, y(0)=0\) is
- \(x=\cos y\)
- \(x=\sin y+q\)
- \(y=\sin x\)
- \(x=\sin y\)
Solution
Given, differential equation, \(\frac{d y}{d x}=\sec y\)
\(\begin{aligned}
& \Rightarrow \int \cos y d y=\int d x \\
& \Rightarrow \sin y=x+c \\
& \therefore \quad y(0)=0 \\
& \Rightarrow c=0 \\
\end{aligned}\)
\(\therefore\) The required solution of differential equation is \(x=\sin y\)
Hence, option (d) is correct.
Asked in: AP EAMCET 2020 (18 Sep Shift 2)
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