Internal problem ID [1986]
Book: Differential Equations by Alfred L. Nelson, Karl W. Folley, Max Coral. 3rd ed. DC heath.
Boston. 1964
Section: Exercise 9, page 38
Problem number: 25.
ODE order: 1.
ODE degree: 1.
CAS Maple gives this as type [[_homogeneous, `class G`], _rational]
\[ \boxed {y \left (x +y^{2}\right )+x \left (-y^{2}+x \right ) y^{\prime }=0} \] With initial conditions \begin {align*} [y \left (2\right ) = 2] \end {align*}
✓ Solution by Maple
Time used: 0.984 (sec). Leaf size: 40
dsolve([y(x)*(x+y(x)^2)+x*(x-y(x)^2)*diff(y(x),x)=0,y(2) = 2],y(x), singsol=all)
\[ y \left (x \right ) = \operatorname {RootOf}\left (-3 \ln \left (x \right )+4 \ln \left (2\right )-4 \ln \left (5\right )+4 \ln \left (\frac {\textit {\_Z}^{2}+3 x}{x}\right )-2 \ln \left (\frac {\textit {\_Z}}{\sqrt {x}}\right )\right ) \]
✗ Solution by Mathematica
Time used: 0.0 (sec). Leaf size: 0
DSolve[{y[x]*(x+y[x]^2)+x*(x-y[x]^2)*y'[x]==0,{y[2]==2}},y[x],x,IncludeSingularSolutions -> True]
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