60.3.139 problem 1143

Internal problem ID [11149]
Book : Differential Gleichungen, E. Kamke, 3rd ed. Chelsea Pub. NY, 1948
Section : Chapter 2, linear second order
Problem number : 1143
Date solved : Tuesday, January 28, 2025 at 05:41:32 PM
CAS classification : [[_2nd_order, _with_linear_symmetries]]

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

✓ Solution by Maple

Time used: 0.192 (sec). Leaf size: 57

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

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

✓ Solution by Mathematica

Time used: 0.071 (sec). Leaf size: 74

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

\[ y(x)\to \sqrt {x} e^{\frac {1}{2}-\frac {b x}{2 a}} \left (c_1 \operatorname {HypergeometricU}\left (1-\frac {c}{b},\frac {3}{2},\frac {b x}{2 a}\right )+c_2 L_{\frac {c}{b}-1}^{\frac {1}{2}}\left (\frac {b x}{2 a}\right )\right ) \]