60.3.166 problem 1170

Internal problem ID [11176]
Book : Differential Gleichungen, E. Kamke, 3rd ed. Chelsea Pub. NY, 1948
Section : Chapter 2, linear second order
Problem number : 1170
Date solved : Monday, January 27, 2025 at 10:47:48 PM
CAS classification : [[_2nd_order, _with_linear_symmetries]]

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

✓ Solution by Maple

Time used: 0.081 (sec). Leaf size: 43

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

\[ y = \frac {c_{2} \operatorname {BesselY}\left (\frac {\sqrt {1-4 b}}{2}, \sqrt {a}\, x \right )+c_{1} \operatorname {BesselJ}\left (\frac {\sqrt {1-4 b}}{2}, \sqrt {a}\, x \right )}{\sqrt {x}} \]

✓ Solution by Mathematica

Time used: 0.035 (sec). Leaf size: 58

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

\[ y(x)\to c_1 j_{\frac {1}{2} \left (\sqrt {1-4 b}-1\right )}\left (\sqrt {a} x\right )+c_2 y_{\frac {1}{2} \left (\sqrt {1-4 b}-1\right )}\left (\sqrt {a} x\right ) \]