29.30.14 problem 873

Internal problem ID [5454]
Book : Ordinary differential equations and their solutions. By George Moseley Murphy. 1960
Section : Various 30
Problem number : 873
Date solved : Monday, January 27, 2025 at 11:24:30 AM
CAS classification : [_quadrature]

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

✓ Solution by Maple

Time used: 0.002 (sec). Leaf size: 15

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

\begin{align*} y \left (x \right ) &= \ln \left (x \right )+c_{1} \\ y \left (x \right ) &= {\mathrm e}^{x} c_{1} \\ \end{align*}

✓ Solution by Mathematica

Time used: 0.011 (sec). Leaf size: 20

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

\begin{align*} y(x)\to c_1 e^x \\ y(x)\to \log (x)+c_1 \\ \end{align*}