Internal problem ID [10191]
Book: An elementary treatise on differential equations by Abraham Cohen. DC heath publishers.
1906
Section: Chapter IV, differential equations of the first order and higher degree than the first. Article
25. Equations solvable for \(y\). Page 52
Problem number: Ex 4.
ODE order: 1.
ODE degree: 1.
CAS Maple gives this as type [[_homogeneous, `class C`], _Riccati]
\[ \boxed {y^{\prime }+2 x y-y^{2}-x^{2}=0} \]
✓ Solution by Maple
Time used: 0.047 (sec). Leaf size: 34
dsolve(diff(y(x),x)+2*x*y(x)=x^2+y(x)^2,y(x), singsol=all)
\[ y \left (x \right ) = \frac {x \,{\mathrm e}^{2 x} c_{1} -{\mathrm e}^{2 x} c_{1} -x -1}{-1+{\mathrm e}^{2 x} c_{1}} \]
✓ Solution by Mathematica
Time used: 0.139 (sec). Leaf size: 29
DSolve[y'[x]+2*x*y[x]==x^2+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*}