Internal problem ID [5291]
Book: Schaums Outline. Theory and problems of Differential Equations, 1st edition. Frank Ayres.
McGraw Hill 1952
Section: Chapter 5. Equations of first order and first degree (Exact equations). Supplemetary
problems. Page 33
Problem number: 26 (d).
ODE order: 1.
ODE degree: 1.
CAS Maple gives this as type [[_homogeneous, `class G`], _rational]
\[ \boxed {y+\left (-x +y^{2}\right ) y^{\prime }=0} \]
✓ Solution by Maple
Time used: 0.0 (sec). Leaf size: 37
dsolve(y(x)+(-x+y(x)^2)*diff(y(x),x)=0,y(x), singsol=all)
\begin{align*} y = \frac {c_{1}}{2}-\frac {\sqrt {c_{1}^{2}-4 x}}{2} y = \frac {c_{1}}{2}+\frac {\sqrt {c_{1}^{2}-4 x}}{2} \end{align*}
✓ Solution by Mathematica
Time used: 0.276 (sec). Leaf size: 54
DSolve[y[x]+(-x+y[x]^2)*y'[x]==0,y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to \frac {1}{2} \left (c_1-\sqrt {-4 x+c_1{}^2}\right ) y(x)\to \frac {1}{2} \left (\sqrt {-4 x+c_1{}^2}+c_1\right ) y(x)\to 0 \end{align*}