Internal problem ID [13081]
Book: Ordinary Differential Equations. An introduction to the fundamentals. Kenneth B. Howell.
second edition. CRC Press. FL, USA. 2020
Section: Chapter 6. Simplifying through simplifiction. Additional exercises. page 114
Problem number: 6.7 (n).
ODE order: 1.
ODE degree: 1.
CAS Maple gives this as type [[_1st_order, _with_linear_symmetries], _Clairaut]
\[ \boxed {y^{\prime }-2 \sqrt {y+x^{2}}=-2 x} \]
✓ Solution by Maple
Time used: 0.016 (sec). Leaf size: 18
dsolve(diff(y(x),x)+2*x=2*sqrt(y(x)+x^2),y(x), singsol=all)
\[ x -\sqrt {y+x^{2}}-c_{1} = 0 \]
✓ Solution by Mathematica
Time used: 0.736 (sec). Leaf size: 35
DSolve[y'[x]+2*x==2*Sqrt[y[x]+x^2],y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to \left (1+e^{c_1}\right ) \left (2 x+1+e^{c_1}\right ) y(x)\to 0 y(x)\to 2 x+1 \end{align*}