60.3.187 problem 1191

Internal problem ID [11197]
Book : Differential Gleichungen, E. Kamke, 3rd ed. Chelsea Pub. NY, 1948
Section : Chapter 2, linear second order
Problem number : 1191
Date solved : Monday, January 27, 2025 at 10:48:29 PM
CAS classification : [[_2nd_order, _with_linear_symmetries]]

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

✓ Solution by Maple

Time used: 0.008 (sec). Leaf size: 23

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

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

✓ Solution by Mathematica

Time used: 0.059 (sec). Leaf size: 72

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

\[ y(x)\to \frac {e^{-x/2} \left (2 (i c_2 x+2 c_1) \sinh \left (\frac {x}{2}\right )-2 (c_1 x+2 i c_2) \cosh \left (\frac {x}{2}\right )\right )}{\sqrt {\pi } \sqrt {-i x} \sqrt {x}} \]