59.1.604 problem 620

Internal problem ID [9776]
Book : Collection of Kovacic problems
Section : section 1
Problem number : 620
Date solved : Monday, January 27, 2025 at 06:14:08 PM
CAS classification : [[_2nd_order, _with_linear_symmetries]]

\begin{align*} x^{2} y^{\prime \prime }+x \left (2 x^{2}+1\right ) y^{\prime }-\left (-10 x^{2}+1\right ) y&=0 \end{align*}

✓ Solution by Maple

Time used: 0.032 (sec). Leaf size: 23

dsolve(x^2*diff(y(x),x$2)+x*(1+2*x^2)*diff(y(x),x)-(1-10*x^2)*y(x)=0,y(x), singsol=all)
 

\[ y = -\frac {x \,{\mathrm e}^{-x^{2}} \left (x^{2}-2\right ) \left (c_{1} -2 c_{2} \right )}{2} \]

✓ Solution by Mathematica

Time used: 0.225 (sec). Leaf size: 51

DSolve[x^2*D[y[x],{x,2}]+x*(1+2*x^2)*D[y[x],x]-(1-10*x^2)*y[x]==0,y[x],x,IncludeSingularSolutions -> True]
 

\[ y(x)\to e^{-x^2} x \left (x^2-2\right ) \left (c_2 \int _1^x\frac {e^{K[1]^2}}{K[1]^3 \left (K[1]^2-2\right )^2}dK[1]+c_1\right ) \]