8.6.16 problem 16

Internal problem ID [786]
Book : Differential equations and linear algebra, 3rd ed., Edwards and Penney
Section : Chapter 1 review problems. Page 78
Problem number : 16
Date solved : Saturday, March 29, 2025 at 10:25:06 PM
CAS classification : [[_homogeneous, `class C`], _Riccati]

\begin{align*} y^{\prime }&=x^{2}-2 x y+y^{2} \end{align*}

✓ Maple. Time used: 0.011 (sec). Leaf size: 31

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

\[ y = \frac {\left (1-x \right ) {\mathrm e}^{2 x}+c_1 \left (x +1\right )}{-{\mathrm e}^{2 x}+c_1} \]

✓ Mathematica. Time used: 0.122 (sec). Leaf size: 29

ode=D[y[x],x] == x^2-2*x*y[x]+y[x]^2; 
ic={}; 
DSolve[{ode,ic},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*}

✓ Sympy. Time used: 0.241 (sec). Leaf size: 26

from sympy import * 
x = symbols("x") 
y = Function("y") 
ode = Eq(-x**2 + 2*x*y(x) - y(x)**2 + Derivative(y(x), x),0) 
ics = {} 
dsolve(ode,func=y(x),ics=ics)
 

\[ y{\left (x \right )} = \frac {C_{1} x + C_{1} - x e^{2 x} + e^{2 x}}{C_{1} - e^{2 x}} \]