60.3.115 problem 1119

Internal problem ID [11125]
Book : Differential Gleichungen, E. Kamke, 3rd ed. Chelsea Pub. NY, 1948
Section : Chapter 2, linear second order
Problem number : 1119
Date solved : Monday, January 27, 2025 at 10:46:21 PM
CAS classification : [[_2nd_order, _with_linear_symmetries]]

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

✓ Solution by Maple

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

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

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

✓ Solution by Mathematica

Time used: 0.162 (sec). Leaf size: 77

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

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