2.46 problem 45

Internal problem ID [7830]
Book : Own collection of miscellaneous problems
Section : section 2.0
Problem number : 45
Date solved : Tuesday, October 22, 2024 at 02:37:59 PM
CAS classification : [[_2nd_order, _with_linear_symmetries]]

Solve

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

2.46.1 Maple step by step solution

2.46.2 Maple trace

Methods for second order ODEs:
 

2.46.3 Maple dsolve solution

Solving time : 0.030 (sec)
Leaf size : 57

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

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

2.46.4 Mathematica DSolve solution

Solving time : 0.0 (sec)
Leaf size : 0

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

Not solved