60.3.183 problem 1187

Internal problem ID [11193]
Book : Differential Gleichungen, E. Kamke, 3rd ed. Chelsea Pub. NY, 1948
Section : Chapter 2, linear second order
Problem number : 1187
Date solved : Monday, January 27, 2025 at 10:48:23 PM
CAS classification : [[_Emden, _Fowler]]

\begin{align*} x^{2} y^{\prime \prime }+a x y^{\prime }+b y&=0 \end{align*}

✓ Solution by Maple

Time used: 0.003 (sec). Leaf size: 52

dsolve(x^2*diff(diff(y(x),x),x)+a*x*diff(y(x),x)+b*y(x)=0,y(x), singsol=all)
 

\[ y = \sqrt {x}\, x^{-\frac {a}{2}} \left (x^{\frac {\sqrt {a^{2}-2 a -4 b +1}}{2}} c_{1} +x^{-\frac {\sqrt {a^{2}-2 a -4 b +1}}{2}} c_{2} \right ) \]

✓ Solution by Mathematica

Time used: 0.042 (sec). Leaf size: 57

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

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