58.2.33 problem 33

Internal problem ID [9156]
Book : Second order enumerated odes
Section : section 2
Problem number : 33
Date solved : Sunday, March 30, 2025 at 02:24:17 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*}

✓ Maple. Time used: 0.021 (sec). Leaf size: 97

ode:=diff(diff(y(x),x),x)-2*tan(x)*diff(y(x),x)+5*y(x) = exp(x^2)*sec(x); 
dsolve(ode,y(x), singsol=all);
 

\[ y = -\frac {\left (\sqrt {\pi }\, \sqrt {6}\, {\mathrm e}^{\frac {3}{2}} \left (i \sin \left (\sqrt {6}\, x \right )-\cos \left (\sqrt {6}\, x \right )\right ) \operatorname {erf}\left (i x -\frac {\sqrt {6}}{2}\right )+\sqrt {\pi }\, \left (i \sin \left (\sqrt {6}\, x \right )+\cos \left (\sqrt {6}\, x \right )\right ) \sqrt {6}\, {\mathrm e}^{\frac {3}{2}} \operatorname {erf}\left (i x +\frac {\sqrt {6}}{2}\right )-24 c_2 \sin \left (\sqrt {6}\, x \right )-24 c_1 \cos \left (\sqrt {6}\, x \right )\right ) \sec \left (x \right )}{24} \]

✓ Mathematica. Time used: 0.25 (sec). Leaf size: 133

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

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

✗ Sympy

from sympy import * 
x = symbols("x") 
y = Function("y") 
ode = Eq(5*y(x) - exp(x**2)/cos(x) - 2*tan(x)*Derivative(y(x), x) + Derivative(y(x), (x, 2)),0) 
ics = {} 
dsolve(ode,func=y(x),ics=ics)
 

NotImplementedError : The given ODE -((5*y(x) + Derivative(y(x), (x, 2)))*cos(x) - exp(x**2))/(2*cos(x)*tan(x)) + Derivative(y(x), x) cannot be solved by the factorable group method