60.3.199 problem 1203

Internal problem ID [11209]
Book : Differential Gleichungen, E. Kamke, 3rd ed. Chelsea Pub. NY, 1948
Section : Chapter 2, linear second order
Problem number : 1203
Date solved : Monday, January 27, 2025 at 10:48:47 PM
CAS classification : [[_2nd_order, _with_linear_symmetries]]

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

✓ Solution by Maple

Time used: 0.006 (sec). Leaf size: 28

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

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

✓ Solution by Mathematica

Time used: 0.084 (sec). Leaf size: 83

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

\[ y(x)\to \frac {2 a x^{3/2} e^{\frac {1}{2}-\frac {a x}{2}} \left ((a c_1 x+2 i c_2) \cosh \left (\frac {a x}{2}\right )-(i a c_2 x+2 c_1) \sinh \left (\frac {a x}{2}\right )\right )}{\sqrt {\pi } (-i a x)^{5/2}} \]