Internal problem ID [13109]
Book: Ordinary Differential Equations. An introduction to the fundamentals. Kenneth B. Howell.
second edition. CRC Press. FL, USA. 2020
Section: Chapter 8. Review exercises for part of part II. page 143
Problem number: 7.
ODE order: 1.
ODE degree: 1.
CAS Maple gives this as type [[_homogeneous, `class C`], _Riccati]
\[ \boxed {y^{\prime }+2 x y-y^{2}=x^{2}} \]
✓ Solution by Maple
Time used: 0.016 (sec). Leaf size: 34
dsolve(diff(y(x),x)=y(x)^2-2*x*y(x)+x^2,y(x), singsol=all)
\[ y = \frac {x \,{\mathrm e}^{2 x} c_{1} -{\mathrm e}^{2 x} c_{1} -x -1}{{\mathrm e}^{2 x} c_{1} -1} \]
✓ Solution by Mathematica
Time used: 0.128 (sec). Leaf size: 29
DSolve[y'[x]==y[x]^2-2*x*y[x]+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*}