60.3.334 problem 1340

Internal problem ID [11344]
Book : Differential Gleichungen, E. Kamke, 3rd ed. Chelsea Pub. NY, 1948
Section : Chapter 2, linear second order
Problem number : 1340
Date solved : Monday, January 27, 2025 at 11:15:42 PM
CAS classification : [[_2nd_order, _with_linear_symmetries]]

\begin{align*} y^{\prime \prime }&=\frac {2 \left (a x +2 b \right ) y^{\prime }}{x \left (a x +b \right )}-\frac {\left (2 a x +6 b \right ) y}{\left (a x +b \right ) x^{2}} \end{align*}

✓ Solution by Maple

Time used: 0.007 (sec). Leaf size: 20

dsolve(diff(diff(y(x),x),x) = 2/x*(a*x+2*b)/(a*x+b)*diff(y(x),x)-(2*a*x+6*b)/(a*x+b)/x^2*y(x),y(x), singsol=all)
 

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

✓ Solution by Mathematica

Time used: 0.213 (sec). Leaf size: 44

DSolve[D[y[x],{x,2}] == -(((6*b + 2*a*x)*y[x])/(x^2*(b + a*x))) + (2*(2*b + a*x)*D[y[x],x])/(x*(b + a*x)),y[x],x,IncludeSingularSolutions -> True]
 

\[ y(x)\to (c_2 x+c_1) \exp \left (-\frac {1}{2} \int _1^x\left (\frac {2 a}{b+a K[1]}-\frac {4}{K[1]}\right )dK[1]\right ) \]