Internal problem ID [3297]
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]
\[ \boxed {y^{\prime }-2 y \tan \left (2 x \right )=2 \sec \left (2 x \right )+2} \]
✓ Solution by Maple
Time used: 0.0 (sec). Leaf size: 32
dsolve(diff(y(x),x) = 2+2*sec(2*x)+2*y(x)*tan(2*x),y(x), singsol=all)
\[ y \left (x \right ) = \left (2 \,\operatorname {csgn}\left (\sec \left (2 x \right )\right ) \left (x +\frac {\sin \left (2 x \right )}{2}\right )+c_{1} \right ) \sqrt {1+\tan \left (2 x \right )^{2}} \]
✓ Solution by Mathematica
Time used: 0.078 (sec). Leaf size: 20
DSolve[y'[x]==2*(1+Sec[2 x]+y[x] Tan[2 x]),y[x],x,IncludeSingularSolutions -> True]
\[ y(x)\to \sec (2 x) (2 x+\sin (2 x)+c_1) \]