Internal problem ID [2070]
Book: Differential Equations by Alfred L. Nelson, Karl W. Folley, Max Coral. 3rd ed. DC heath.
Boston. 1964
Section: Exercise 12, page 46
Problem number: 40.
ODE order: 1.
ODE degree: 1.
CAS Maple gives this as type [[_homogeneous, `class A`], _rational, _Bernoulli]
\[ \boxed {y x -y^{2}-y^{\prime } x^{2}=0} \] With initial conditions \begin {align*} [y \left (1\right ) = 1] \end {align*}
✓ Solution by Maple
Time used: 0.016 (sec). Leaf size: 12
dsolve([(x*y(x)-y(x)^2)-x^2*diff(y(x),x)=0,y(1) = 1],y(x), singsol=all)
\[ y \left (x \right ) = \frac {x}{\ln \left (x \right )+1} \]
✓ Solution by Mathematica
Time used: 0.137 (sec). Leaf size: 13
DSolve[{(x*y[x]-y[x]^2)-x^2*y'[x]==0,{y[1]==1}},y[x],x,IncludeSingularSolutions -> True]
\[ y(x)\to \frac {x}{\log (x)+1} \]