7.7.16 problem 16

Internal problem ID [194]
Book : Elementary Differential Equations. By C. Henry Edwards, David E. Penney and David Calvis. 6th edition. 2008
Section : Chapter 1. First order differential equations. Review problems at page 98
Problem number : 16
Date solved : Friday, February 07, 2025 at 08:04:20 AM
CAS classification : [[_homogeneous, `class C`], _Riccati]

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

✓ Solution by Maple

Time used: 0.026 (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: 0.144 (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*}