60.3.177 problem 1181

Internal problem ID [11187]
Book : Differential Gleichungen, E. Kamke, 3rd ed. Chelsea Pub. NY, 1948
Section : Chapter 2, linear second order
Problem number : 1181
Date solved : Monday, January 27, 2025 at 10:48:11 PM
CAS classification : [[_2nd_order, _exact, _linear, _homogeneous]]

\begin{align*} x^{2} y^{\prime \prime }+\left (3 x -1\right ) y^{\prime }+y&=0 \end{align*}

✓ Solution by Maple

Time used: 0.002 (sec). Leaf size: 25

dsolve(x^2*diff(diff(y(x),x),x)+(3*x-1)*diff(y(x),x)+y(x)=0,y(x), singsol=all)
 

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

✓ Solution by Mathematica

Time used: 0.102 (sec). Leaf size: 30

DSolve[y[x] + (-1 + 3*x)*D[y[x],x] + x^2*D[y[x],{x,2}] == 0,y[x],x,IncludeSingularSolutions -> True]
 

\[ y(x)\to \frac {e^{1-\frac {1}{x}} \left (c_1-e c_2 \operatorname {ExpIntegralEi}\left (\frac {1}{x}\right )\right )}{x} \]