Internal problem ID [136]
Book: Differential equations and linear algebra, 3rd ed., Edwards and Penney
Section: Chapter 1 review problems. Page 78
Problem number: 16.
ODE order: 1.
ODE degree: 1.
CAS Maple gives this as type [[_homogeneous, `class C`], _Riccati]
\[ \boxed {2 y x +y^{\prime }-y^{2}=x^{2}} \]
✓ Solution by Maple
Time used: 0.016 (sec). Leaf size: 33
dsolve(diff(y(x),x) = x^2-2*x*y(x)+y(x)^2,y(x), singsol=all)
\[ y \left (x \right ) = \frac {x \,{\mathrm e}^{-2 x} c_{1} +{\mathrm e}^{-2 x} c_{1} -x +1}{{\mathrm e}^{-2 x} c_{1} -1} \]
✓ Solution by Mathematica
Time used: 0.127 (sec). Leaf size: 29
DSolve[y'[x] == x^2-2*x*y[x]+y[x]^2,y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to x+\frac {1}{\frac {1}{2}+c_1 e^{2 x}}-1 y(x)\to x-1 \end{align*}