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 : Monday, January 27, 2025 at 03:05:23 AM
CAS classification : [[_homogeneous, `class C`], _Riccati]

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

✓ Solution by Maple

Time used: 0.015 (sec). Leaf size: 31

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

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

✓ Solution by Mathematica

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

DSolve[D[y[x],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*}