60.3.52 problem 1053

Internal problem ID [11062]
Book : Differential Gleichungen, E. Kamke, 3rd ed. Chelsea Pub. NY, 1948
Section : Chapter 2, linear second order
Problem number : 1053
Date solved : Monday, January 27, 2025 at 10:42:55 PM
CAS classification : [[_2nd_order, _with_linear_symmetries]]

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

✓ Solution by Maple

Time used: 0.004 (sec). Leaf size: 35

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

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

✓ Solution by Mathematica

Time used: 0.069 (sec). Leaf size: 56

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

\[ y(x)\to \frac {e^{-\frac {a x^2}{2}-\sqrt {a} x} \left (c_2 e^{2 \sqrt {a} x}+2 \sqrt {a} c_1\right )}{2 \sqrt {a}} \]