60.3.340 problem 1346

Internal problem ID [11350]
Book : Differential Gleichungen, E. Kamke, 3rd ed. Chelsea Pub. NY, 1948
Section : Chapter 2, linear second order
Problem number : 1346
Date solved : Monday, January 27, 2025 at 11:17:39 PM
CAS classification : [[_2nd_order, _with_linear_symmetries]]

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

✓ Solution by Maple

Time used: 0.007 (sec). Leaf size: 25

dsolve(diff(diff(y(x),x),x) = 1/x^2*(a+b)*diff(y(x),x)-((a+b)*x+a*b)/x^4*y(x),y(x), singsol=all)
 

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

✓ Solution by Mathematica

Time used: 0.158 (sec). Leaf size: 41

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

\[ y(x)\to \frac {c_2 x e^{1-\frac {a}{x}}}{a-b}+c_1 x e^{-\frac {b+x}{x}} \]