Internal problem ID [5141]
Book: THEORY OF DIFFERENTIAL EQUATIONS IN ENGINEERING AND MECHANICS. K.T.
CHAU, CRC Press. Boca Raton, FL. 2018
Section: Chapter 3. Ordinary Differential Equations. Section 3.6 Summary and Problems. Page
218
Problem number: Problem 3.33.
ODE order: 1.
ODE degree: 1.
CAS Maple gives this as type [[_homogeneous, class D], _rational, _Riccati]
Solve \begin {gather*} \boxed {x y^{\prime }-y-x^{2}-y^{2}=0} \end {gather*}
✓ Solution by Maple
Time used: 0.005 (sec). Leaf size: 10
dsolve(x*diff(y(x),x)-y(x)=(x^2+y(x)^2),y(x), singsol=all)
\[ y \relax (x ) = \tan \left (c_{1}+x \right ) x \]
✓ Solution by Mathematica
Time used: 0.186 (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*}