60.3.198 problem 1202

Internal problem ID [11208]
Book : Differential Gleichungen, E. Kamke, 3rd ed. Chelsea Pub. NY, 1948
Section : Chapter 2, linear second order
Problem number : 1202
Date solved : Monday, January 27, 2025 at 10:48:45 PM
CAS classification : [[_2nd_order, _with_linear_symmetries]]

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

✓ Solution by Maple

Time used: 0.004 (sec). Leaf size: 14

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

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

✓ Solution by Mathematica

Time used: 0.053 (sec). Leaf size: 24

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

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