60.3.118 problem 1122

Internal problem ID [11128]
Book : Differential Gleichungen, E. Kamke, 3rd ed. Chelsea Pub. NY, 1948
Section : Chapter 2, linear second order
Problem number : 1122
Date solved : Monday, January 27, 2025 at 10:46:26 PM
CAS classification : [[_2nd_order, _with_linear_symmetries]]

\begin{align*} x y^{\prime \prime }-\left (x^{2}-x -2\right ) y^{\prime }-x \left (x +3\right ) y&=0 \end{align*}

✓ Solution by Maple

Time used: 0.574 (sec). Leaf size: 28

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

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

✓ Solution by Mathematica

Time used: 0.338 (sec). Leaf size: 45

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

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