Internal problem ID [6717]
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]]
\[ \boxed {y^{\prime \prime }-2 \tan \left (x \right ) y^{\prime }+5 y-{\mathrm e}^{x^{2}} \sec \left (x \right )=0} \]
✓ Solution by Maple
Time used: 0.032 (sec). Leaf size: 96
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)
\[ y \left (x \right ) = \sec \left (x \right ) \sin \left (x \sqrt {6}\right ) c_{2} +\sec \left (x \right ) \cos \left (x \sqrt {6}\right ) c_{1} -\frac {\left (\left (i \sin \left (x \sqrt {6}\right )-\cos \left (x \sqrt {6}\right )\right ) \operatorname {erf}\left (i x -\frac {\sqrt {6}}{2}\right )+\left (i \sin \left (x \sqrt {6}\right )+\cos \left (x \sqrt {6}\right )\right ) \operatorname {erf}\left (i x +\frac {\sqrt {6}}{2}\right )\right ) \sec \left (x \right ) \sqrt {6}\, \sqrt {\pi }\, {\mathrm e}^{\frac {3}{2}}}{24} \]
✓ Solution by Mathematica
Time used: 0.104 (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*}