60.3.111 problem 1115

Internal problem ID [11121]
Book : Differential Gleichungen, E. Kamke, 3rd ed. Chelsea Pub. NY, 1948
Section : Chapter 2, linear second order
Problem number : 1115
Date solved : Tuesday, January 28, 2025 at 05:41:16 PM
CAS classification : [[_2nd_order, _with_linear_symmetries]]

\begin{align*} x y^{\prime \prime }-\left (3 x -2\right ) y^{\prime }-\left (2 x -3\right ) y&=0 \end{align*}

✓ Solution by Maple

Time used: 0.050 (sec). Leaf size: 47

dsolve(x*diff(diff(y(x),x),x)-(3*x-2)*diff(y(x),x)-(2*x-3)*y(x)=0,y(x), singsol=all)
 

\[ y = {\mathrm e}^{-\frac {x \left (-3+\sqrt {17}\right )}{2}} \left (\operatorname {KummerU}\left (1-\frac {6 \sqrt {17}}{17}, 2, \sqrt {17}\, x \right ) c_{2} +\operatorname {KummerM}\left (1-\frac {6 \sqrt {17}}{17}, 2, \sqrt {17}\, x \right ) c_{1} \right ) \]

✓ Solution by Mathematica

Time used: 0.110 (sec). Leaf size: 63

DSolve[(3 - 2*x)*y[x] - (-2 + 3*x)*D[y[x],x] + x*D[y[x],{x,2}] == 0,y[x],x,IncludeSingularSolutions -> True]
 

\[ y(x)\to e^{-\frac {1}{2} \left (\sqrt {17}-3\right ) x} \left (c_2 \operatorname {Hypergeometric1F1}\left (1-\frac {6}{\sqrt {17}},2,\sqrt {17} x\right )+c_1 \operatorname {HypergeometricU}\left (1-\frac {6}{\sqrt {17}},2,\sqrt {17} x\right )\right ) \]