Question

Find the solution to the differential equation dy/dx = (1+x^2 ) / (cos (y)) with initial condition, y(0) = pi/2 . Make sure to isolate y.

Answer 1

\[\begin{align*}\frac{dy}{dx}&=\frac{1+x^2}{\cos y}\\
\cos y~dy&=(1+x^2)~dx
\end{align*}\]
Integrate both sides, you get
\[\sin y=x+\frac{1}{3}x^3+C\]
Plug in the given initial condition to solve for \(C\).

Answer 2

Thanks A lot.

Answer 3

yw