Internal problem ID [5277]
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: 25 (a).
ODE order: 1.
ODE degree: 1.
CAS Maple gives this as type [[_homogeneous, `class D`], _rational, _Bernoulli]
\[ \boxed {-y^{2}+y y^{\prime }=x^{2}-x} \]
✓ Solution by Maple
Time used: 0.016 (sec). Leaf size: 37
dsolve((x-x^2-y(x)^2)+y(x)*diff(y(x),x)=0,y(x), singsol=all)
\begin{align*} y = \sqrt {c_{1} {\mathrm e}^{2 x}-x^{2}} y = -\sqrt {c_{1} {\mathrm e}^{2 x}-x^{2}} \end{align*}
✓ Solution by Mathematica
Time used: 4.613 (sec). Leaf size: 47
DSolve[(x-x^2-y[x]^2)+y[x]*y'[x]==0,y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to -\sqrt {-x^2+c_1 e^{2 x}} y(x)\to \sqrt {-x^2+c_1 e^{2 x}} \end{align*}