Internal problem ID [6718]
Book: Second order enumerated odes
Section: section 2
Problem number: 33.
ODE order: 2.
ODE degree: 1.
CAS Maple gives this as type [[_2nd_order, _linear, _nonhomogeneous]]
Solve \begin {gather*} \boxed {y^{\prime \prime }-2 \tan \relax (x ) y^{\prime }+5 y-{\mathrm e}^{x^{2}} \sec \relax (x )=0} \end {gather*}
✓ Solution by Maple
Time used: 0.016 (sec). Leaf size: 102
dsolve(diff(y(x),x$2)-2*tan(x)*diff(y(x),x)+5*y(x)=exp(x^2)*sec(x),y(x), singsol=all)
\[ y \relax (x ) = \frac {\sin \left (\sqrt {6}\, x \right ) c_{2}}{\cos \relax (x )}+\frac {\cos \left (\sqrt {6}\, x \right ) c_{1}}{\cos \relax (x )}-\frac {\sqrt {6}\, \left (\left (i \sin \left (\sqrt {6}\, x \right )-\cos \left (\sqrt {6}\, x \right )\right ) \erf \left (i x -\frac {\sqrt {6}}{2}\right )+\left (i \sin \left (\sqrt {6}\, x \right )+\cos \left (\sqrt {6}\, x \right )\right ) \erf \left (i x +\frac {\sqrt {6}}{2}\right )\right ) {\mathrm e}^{\frac {3}{2}} \sqrt {\pi }}{24 \cos \relax (x )} \]
✓ Solution by Mathematica
Time used: 0.174 (sec). Leaf size: 107
DSolve[y''[x]-2*Tan[x]*y'[x]+5*y[x]==Exp[x^2]*Sec[x],y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to \frac {1}{24} e^{-i \sqrt {6} x} \sec (x) \left (-e^{3/2} \sqrt {6 \pi } \left (\text {Erf}\left (\sqrt {\frac {3}{2}}-i x\right )+e^{2 i \sqrt {6} x} \text {Erf}\left (\sqrt {\frac {3}{2}}+i x\right )\right )-2 i \sqrt {6} c_2 e^{2 i \sqrt {6} x}+24 c_1\right ) \\ \end{align*}