60.3.96 problem 1100

Internal problem ID [11106]
Book : Differential Gleichungen, E. Kamke, 3rd ed. Chelsea Pub. NY, 1948
Section : Chapter 2, linear second order
Problem number : 1100
Date solved : Monday, January 27, 2025 at 10:45:52 PM
CAS classification : [[_2nd_order, _linear, _nonhomogeneous]]

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

✓ Solution by Maple

Time used: 0.009 (sec). Leaf size: 24

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

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

✓ Solution by Mathematica

Time used: 0.032 (sec). Leaf size: 37

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

\[ y(x)\to \frac {e^{-x} \left (e^{2 x} (2 x-1+2 c_2)+4 c_1\right )}{4 x} \]