60.1.134 problem 135

Internal problem ID [10148]
Book : Differential Gleichungen, E. Kamke, 3rd ed. Chelsea Pub. NY, 1948
Section : Chapter 1, linear first order
Problem number : 135
Date solved : Monday, January 27, 2025 at 06:30:01 PM
CAS classification : [_separable]

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

✓ Solution by Maple

Time used: 0.002 (sec). Leaf size: 11

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

\[ y = c_{1} {\mathrm e}^{\frac {1}{x}} x \]

✓ Solution by Mathematica

Time used: 0.036 (sec). Leaf size: 21

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

\begin{align*} y(x)\to c_1 e^{\frac {1}{x}-1} x \\ y(x)\to 0 \\ \end{align*}