2.47 problem 46

Internal problem ID [7831]
Book : Own collection of miscellaneous problems
Section : section 2.0
Problem number : 46
Date solved : Tuesday, October 22, 2024 at 02:38:00 PM
CAS classification : [[_2nd_order, _with_linear_symmetries]]

Solve

\begin{align*} y^{\prime \prime }-x^{2} y^{\prime }-x^{3} y-x^{4}-x^{2}&=0 \end{align*}

2.47.1 Maple step by step solution

2.47.2 Maple trace

Methods for second order ODEs:
 

2.47.3 Maple dsolve solution

Solving time : 0.091 (sec)
Leaf size : 74

dsolve(diff(diff(y(x),x),x)-x^2*diff(y(x),x)-x^3*y(x)-x^4-x^2 = 0, 
       y(x),singsol=all)
 

\[ y = {\mathrm e}^{-\frac {x \left (x -2\right )}{2}} \operatorname {HeunT}\left (2 \,3^{{2}/{3}}, -3, -3 \,3^{{1}/{3}}, \frac {3^{{2}/{3}} \left (x +1\right )}{3}\right ) c_2 +{\mathrm e}^{\frac {1}{3} x^{3}+\frac {1}{2} x^{2}-x} \operatorname {HeunT}\left (2 \,3^{{2}/{3}}, 3, -3 \,3^{{1}/{3}}, -\frac {3^{{2}/{3}} \left (x +1\right )}{3}\right ) c_1 -x \]

2.47.4 Mathematica DSolve solution

Solving time : 0.0 (sec)
Leaf size : 0

DSolve[{D[y[x],{x,2}]-x^2*D[y[x],x]-x^3*y[x]-x^4-x^2==0,{}}, 
       y[x],x,IncludeSingularSolutions->True]
 

Not solved