73.5.26 problem 6.7 (n)

Internal problem ID [15137]
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)
Date solved : Tuesday, January 28, 2025 at 07:36:26 AM
CAS classification : [[_1st_order, _with_linear_symmetries], _Clairaut]

\begin{align*} y^{\prime }+2 x&=2 \sqrt {y+x^{2}} \end{align*}

✓ Solution by Maple

Time used: 0.064 (sec). Leaf size: 18

dsolve(diff(y(x),x)+2*x=2*sqrt(y(x)+x^2),y(x), singsol=all)
 

\[ x -\sqrt {x^{2}+y}-c_{1} = 0 \]

✓ Solution by Mathematica

Time used: 0.751 (sec). Leaf size: 35

DSolve[D[y[x],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*}