6.16 problem 16

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]

Solve \begin {gather*} \boxed {y^{\prime }-x^{2}+2 y x -y^{2}=0} \end {gather*}

Solution by Maple

Time used: 0.016 (sec). Leaf size: 34

dsolve(diff(y(x),x) = x^2-2*x*y(x)+y(x)^2,y(x), singsol=all)
 

\[ y \relax (x ) = \frac {x \,{\mathrm e}^{2 x} c_{1}-{\mathrm e}^{2 x} c_{1}-x -1}{{\mathrm e}^{2 x} c_{1}-1} \]

Solution by Mathematica

Time used: 0.126 (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*}