58.2.33 problem 33

Internal problem ID [9156]
Book : Second order enumerated odes
Section : section 2
Problem number : 33
Date solved : Monday, January 27, 2025 at 05:50:59 PM
CAS classification : [[_2nd_order, _linear, _nonhomogeneous]]

\begin{align*} y^{\prime \prime }-2 \tan \left (x \right ) y^{\prime }+5 y&={\mathrm e}^{x^{2}} \sec \left (x \right ) \end{align*}

✓ Solution by Maple

Time used: 0.014 (sec). Leaf size: 97

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)
 

\[ y = -\frac {\left ({\mathrm e}^{\frac {3}{2}} \left (i \sin \left (\sqrt {6}\, x \right )-\cos \left (\sqrt {6}\, x \right )\right ) \sqrt {\pi }\, \sqrt {6}\, \operatorname {erf}\left (i x -\frac {\sqrt {6}}{2}\right )+{\mathrm e}^{\frac {3}{2}} \left (i \sin \left (\sqrt {6}\, x \right )+\cos \left (\sqrt {6}\, x \right )\right ) \sqrt {\pi }\, \sqrt {6}\, \operatorname {erf}\left (i x +\frac {\sqrt {6}}{2}\right )-24 \sin \left (\sqrt {6}\, x \right ) c_{2} -24 \cos \left (\sqrt {6}\, x \right ) c_{1} \right ) \sec \left (x \right )}{24} \]

✓ Solution by Mathematica

Time used: 0.250 (sec). Leaf size: 133

DSolve[D[y[x],{x,2}]-2*Tan[x]*D[y[x],x]+5*y[x]==Exp[x^2]*Sec[x],y[x],x,IncludeSingularSolutions -> True]
 

\[ y(x)\to \frac {1}{12} e^{-i \sqrt {6} x} \sec (x) \left (12 \int _1^x\frac {i e^{K[1] \left (K[1]+i \sqrt {6}\right )}}{2 \sqrt {6}}dK[1]-i \sqrt {6} e^{2 i \sqrt {6} x} \int _1^xe^{K[2] \left (K[2]-i \sqrt {6}\right )}dK[2]-i \sqrt {6} c_2 e^{2 i \sqrt {6} x}+12 c_1\right ) \]