29.2.8 problem 33

Internal problem ID [4641]
Book : Ordinary differential equations and their solutions. By George Moseley Murphy. 1960
Section : Various 2
Problem number : 33
Date solved : Monday, January 27, 2025 at 09:29:06 AM
CAS classification : [_linear]

\begin{align*} y^{\prime }&=2+2 \sec \left (2 x \right )+2 y \tan \left (2 x \right ) \end{align*}

✓ Solution by Maple

Time used: 0.003 (sec). Leaf size: 24

dsolve(diff(y(x),x) = 2+2*sec(2*x)+2*y(x)*tan(2*x),y(x), singsol=all)
 

\[ y \left (x \right ) = \sec \left (2 x \right ) \left (\operatorname {csgn}\left (\sec \left (2 x \right )\right ) c_{1} +\sin \left (2 x \right )+2 x \right ) \]

✓ Solution by Mathematica

Time used: 0.065 (sec). Leaf size: 20

DSolve[D[y[x],x]==2*(1+Sec[2 x]+y[x] Tan[2 x]),y[x],x,IncludeSingularSolutions -> True]
 

\[ y(x)\to \sec (2 x) (2 x+\sin (2 x)+c_1) \]