60.3.124 problem 1128

Internal problem ID [11134]
Book : Differential Gleichungen, E. Kamke, 3rd ed. Chelsea Pub. NY, 1948
Section : Chapter 2, linear second order
Problem number : 1128
Date solved : Monday, January 27, 2025 at 10:46:38 PM
CAS classification : [[_2nd_order, _with_linear_symmetries]]

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

✓ Solution by Maple

Time used: 0.118 (sec). Leaf size: 33

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

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

✓ Solution by Mathematica

Time used: 0.186 (sec). Leaf size: 37

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

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