Internal problem ID [2826]
Book: Ordinary differential equations and their solutions. By George Moseley Murphy.
1960
Section: Various 3
Problem number: 71.
ODE order: 1.
ODE degree: 1.
CAS Maple gives this as type [_linear]
Solve \begin {gather*} \boxed {y^{\prime }-\sin \relax (x ) \left (2 \left (\sec ^{2}\relax (x )\right )-y\right )=0} \end {gather*}
✓ Solution by Maple
Time used: 0.003 (sec). Leaf size: 29
dsolve(diff(y(x),x) = sin(x)*(2*sec(x)^2-y(x)),y(x), singsol=all)
\[ y \relax (x ) = \left (\int \frac {4 \,{\mathrm e}^{-\cos \relax (x )} \sin \relax (x )}{\cos \left (2 x \right )+1}d x +c_{1}\right ) {\mathrm e}^{\cos \relax (x )} \]
✓ Solution by Mathematica
Time used: 0.125 (sec). Leaf size: 25
DSolve[y'[x]==Sin[x](2 Sec[x]^2-y[x]),y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to 2 \sec (x)+e^{\cos (x)} (2 \text {Ei}(-\cos (x))+c_1) \\ \end{align*}