60.3.132 problem 1136

Internal problem ID [11142]
Book : Differential Gleichungen, E. Kamke, 3rd ed. Chelsea Pub. NY, 1948
Section : Chapter 2, linear second order
Problem number : 1136
Date solved : Monday, January 27, 2025 at 10:46:49 PM
CAS classification : [[_2nd_order, _with_linear_symmetries]]

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

✓ Solution by Maple

Time used: 0.004 (sec). Leaf size: 16

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

\[ y = {\mathrm e}^{\frac {x}{2}} \left (c_{1} +\operatorname {Ei}_{1}\left (x \right ) c_{2} \right ) \]

✓ Solution by Mathematica

Time used: 0.226 (sec). Leaf size: 41

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

\[ y(x)\to e^{\frac {x+1}{2}} \left (c_2 \int _1^x\frac {e^{-K[1]-1}}{K[1]}dK[1]+c_1\right ) \]