15.19.6 problem 6

Internal problem ID [3290]
Book : Differential Equations by Alfred L. Nelson, Karl W. Folley, Max Coral. 3rd ed. DC heath. Boston. 1964
Section : Exercise 37, page 171
Problem number : 6
Date solved : Monday, January 27, 2025 at 07:31:11 AM
CAS classification : [`y=_G(x,y')`]

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

✗ Solution by Maple

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

\[ \text {No solution found} \]

✗ Solution by Mathematica

Time used: 0.000 (sec). Leaf size: 0

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

Not solved