Internal problem ID [7474]
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]]
\[ \boxed {y^{\prime \prime }-2 \tan \left (x \right ) y^{\prime }+5 y={\mathrm e}^{x^{2}} \sec \left (x \right )} \]
✓ Solution by Maple
Time used: 0.015 (sec). Leaf size: 101
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)
\[ y \left (x \right ) = -\frac {\left (\sqrt {6}\, {\mathrm e}^{\frac {3}{2}} \sqrt {\pi }\, \left (i \sin \left (\sqrt {6}\, x \right )-\cos \left (\sqrt {6}\, x \right )\right ) \operatorname {erf}\left (i x -\frac {\sqrt {6}}{2}\right )+\sqrt {6}\, {\mathrm e}^{\frac {3}{2}} \left (i \sin \left (\sqrt {6}\, x \right )+\cos \left (\sqrt {6}\, x \right )\right ) \sqrt {\pi }\, \operatorname {erf}\left (i x +\frac {\sqrt {6}}{2}\right )-24 \sin \left (\sqrt {6}\, x \right ) c_{2} -24 \cos \left (\sqrt {6}\, x \right ) c_{1} \right ) \sec \left (x \right )}{24} \]
✓ Solution by Mathematica
Time used: 0.249 (sec). Leaf size: 118
DSolve[y''[x]-2*Tan[x]*y'[x]+5*y[x]==Exp[x^2]*Sec[x],y[x],x,IncludeSingularSolutions -> True]
\[ y(x)\to \frac {1}{24} e^{-i \sqrt {6} x} \sec (x) \left (-e^{3/2} \sqrt {6 \pi } \text {erf}\left (\sqrt {\frac {3}{2}}-i x\right )-\sqrt {6 \pi } e^{\frac {3}{2}+2 i \sqrt {6} x} \text {erf}\left (\sqrt {\frac {3}{2}}+i x\right )-2 i \sqrt {6} c_2 e^{2 i \sqrt {6} x}+24 c_1\right ) \]