60.3.108 problem 1112

Internal problem ID [11118]
Book : Differential Gleichungen, E. Kamke, 3rd ed. Chelsea Pub. NY, 1948
Section : Chapter 2, linear second order
Problem number : 1112
Date solved : Monday, January 27, 2025 at 10:46:11 PM
CAS classification : [[_2nd_order, _with_linear_symmetries]]

\begin{align*} x y^{\prime \prime }-\left (1+x \right ) y^{\prime }-2 \left (x -1\right ) y&=0 \end{align*}

✓ Solution by Maple

Time used: 0.006 (sec). Leaf size: 22

dsolve(x*diff(diff(y(x),x),x)-(x+1)*diff(y(x),x)-2*(x-1)*y(x)=0,y(x), singsol=all)
 

\[ y = {\mathrm e}^{2 x} c_{1} +c_{2} {\mathrm e}^{-x} \left (3 x +1\right ) \]

✓ Solution by Mathematica

Time used: 0.243 (sec). Leaf size: 37

DSolve[-2*(-1 + x)*y[x] - (1 + x)*D[y[x],x] + x*D[y[x],{x,2}] == 0,y[x],x,IncludeSingularSolutions -> True]
 

\[ y(x)\to e^{2 x+\frac {1}{2}} \left (c_2 \int _1^xe^{-3 K[1]} K[1]dK[1]+c_1\right ) \]