60.3.155 problem 1159

Internal problem ID [11165]
Book : Differential Gleichungen, E. Kamke, 3rd ed. Chelsea Pub. NY, 1948
Section : Chapter 2, linear second order
Problem number : 1159
Date solved : Monday, January 27, 2025 at 10:47:31 PM
CAS classification : [[_2nd_order, _exact, _linear, _nonhomogeneous]]

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

✓ Solution by Maple

Time used: 0.001 (sec). Leaf size: 19

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

\[ y = c_{2} x +\frac {a \,x^{2}}{3}+\frac {c_{1}}{x} \]

✓ Solution by Mathematica

Time used: 0.016 (sec). Leaf size: 24

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

\[ y(x)\to \frac {a x^2}{3}+c_2 x+\frac {c_1}{x} \]