60.3.45 problem 1046

Internal problem ID [11055]
Book : Differential Gleichungen, E. Kamke, 3rd ed. Chelsea Pub. NY, 1948
Section : Chapter 2, linear second order
Problem number : 1046
Date solved : Tuesday, January 28, 2025 at 05:40:44 PM
CAS classification : [[_2nd_order, _with_linear_symmetries]]

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

✓ Solution by Maple

Time used: 0.138 (sec). Leaf size: 31

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

\[ y = x \left (\operatorname {KummerM}\left (\frac {1}{2}-\frac {a}{4}, \frac {3}{2}, x^{2}\right ) c_{1} +\operatorname {KummerU}\left (\frac {1}{2}-\frac {a}{4}, \frac {3}{2}, x^{2}\right ) c_{2} \right ) \]

✓ Solution by Mathematica

Time used: 0.021 (sec). Leaf size: 31

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

\[ y(x)\to c_1 \operatorname {HermiteH}\left (\frac {a}{2},x\right )+c_2 \operatorname {Hypergeometric1F1}\left (-\frac {a}{4},\frac {1}{2},x^2\right ) \]