60.3.175 problem 1179

Internal problem ID [11185]
Book : Differential Gleichungen, E. Kamke, 3rd ed. Chelsea Pub. NY, 1948
Section : Chapter 2, linear second order
Problem number : 1179
Date solved : Monday, January 27, 2025 at 10:48:06 PM
CAS classification : [[_2nd_order, _with_linear_symmetries]]

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

✓ Solution by Maple

Time used: 0.006 (sec). Leaf size: 19

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

\[ y = x \left (c_{1} \sin \left (a x \right )+c_{2} \cos \left (a x \right )\right ) \]

✓ Solution by Mathematica

Time used: 0.038 (sec). Leaf size: 38

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

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