60.3.161 problem 1165

Internal problem ID [11171]
Book : Differential Gleichungen, E. Kamke, 3rd ed. Chelsea Pub. NY, 1948
Section : Chapter 2, linear second order
Problem number : 1165
Date solved : Monday, January 27, 2025 at 10:47:40 PM
CAS classification : [[_2nd_order, _exact, _linear, _homogeneous]]

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

✓ Solution by Maple

Time used: 0.004 (sec). Leaf size: 19

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

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

✓ Solution by Mathematica

Time used: 0.177 (sec). Leaf size: 31

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

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