Internal problem ID [2788]
Book: Ordinary differential equations and their solutions. By George Moseley Murphy.
1960
Section: Various 2
Problem number: 33.
ODE order: 1.
ODE degree: 1.
CAS Maple gives this as type [_linear]
Solve \begin {gather*} \boxed {y^{\prime }-2-2 \sec \left (2 x \right )-2 y \tan \left (2 x \right )=0} \end {gather*}
✓ Solution by Maple
Time used: 0.004 (sec). Leaf size: 48
dsolve(diff(y(x),x) = 2+2*sec(2*x)+2*y(x)*tan(2*x),y(x), singsol=all)
\[ y \relax (x ) = \sqrt {1+\tan ^{2}\left (2 x \right )}\, c_{1}+\sqrt {2}\, \sqrt {\frac {1}{\cos \left (4 x \right )+1}}\, \cos \left (2 x \right ) \left (2 x +\sin \left (2 x \right )\right ) \sqrt {1+\tan ^{2}\left (2 x \right )} \]
✓ Solution by Mathematica
Time used: 0.08 (sec). Leaf size: 20
DSolve[y'[x]==2*(1+Sec[2 x]+y[x] Tan[2 x]),y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to \sec (2 x) (2 x+\sin (2 x)+c_1) \\ \end{align*}