60.3.133 problem 1137

Internal problem ID [11143]
Book : Differential Gleichungen, E. Kamke, 3rd ed. Chelsea Pub. NY, 1948
Section : Chapter 2, linear second order
Problem number : 1137
Date solved : Tuesday, January 28, 2025 at 05:41:28 PM
CAS classification : [[_2nd_order, _with_linear_symmetries]]

\begin{align*} 4 x y^{\prime \prime }+4 y-\left (x +2\right ) y+l y&=0 \end{align*}

✓ Solution by Maple

Time used: 0.041 (sec). Leaf size: 25

dsolve(4*x*diff(diff(y(x),x),x)+4*y(x)-(x+2)*y(x)+l*y(x)=0,y(x), singsol=all)
 

\[ y = c_{1} \operatorname {WhittakerM}\left (\frac {l}{4}+\frac {1}{2}, \frac {1}{2}, x\right )+c_{2} \operatorname {WhittakerW}\left (\frac {l}{4}+\frac {1}{2}, \frac {1}{2}, x\right ) \]

✓ Solution by Mathematica

Time used: 0.133 (sec). Leaf size: 48

DSolve[4*y[x] + l*y[x] - (2 + x)*y[x] + 4*x*D[y[x],{x,2}] == 0,y[x],x,IncludeSingularSolutions -> True]
 

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