59.1.459 problem 474

Internal problem ID [9631]
Book : Collection of Kovacic problems
Section : section 1
Problem number : 474
Date solved : Monday, January 27, 2025 at 06:04:49 PM
CAS classification : [[_2nd_order, _with_linear_symmetries]]

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

✓ Solution by Maple

Time used: 0.006 (sec). Leaf size: 15

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

\[ y = x \left (c_{1} \sinh \left (x \right )+c_{2} \cosh \left (x \right )\right ) \]

✓ Solution by Mathematica

Time used: 0.028 (sec). Leaf size: 25

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

\[ y(x)\to c_1 e^{-x} x+\frac {1}{2} c_2 e^x x \]