Internal problem ID [10147]
Book: An elementary treatise on differential equations by Abraham Cohen. DC heath publishers.
1906
Section: Chapter 2, differential equations of the first order and the first degree. Article 16. Integrating
factors by inspection. Page 23
Problem number: Ex 6.
ODE order: 1.
ODE degree: 1.
CAS Maple gives this as type [[_homogeneous, class D], _rational, _Riccati]
Solve \begin {gather*} \boxed {y^{\prime } x -y-y^{2}-x^{2}=0} \end {gather*}
✓ Solution by Maple
Time used: 0.0 (sec). Leaf size: 10
dsolve(x*diff(y(x),x)-y(x)=x^2+y(x)^2,y(x), singsol=all)
\[ y \relax (x ) = \tan \left (x +c_{1}\right ) x \]
✓ Solution by Mathematica
Time used: 0.203 (sec). Leaf size: 12
DSolve[x*y'[x]-y[x]==x^2+y[x]^2,y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to x \tan (x+c_1) \\ \end{align*}