Internal problem ID [12340]
Book: Ordinary Differential Equations by Charles E. Roberts, Jr. CRC Press. 2010
Section: Chapter 2. The Initial Value Problem. Exercises 2.2, page 53
Problem number: 24.
ODE order: 1.
ODE degree: 1.
CAS Maple gives this as type [[_1st_order, _with_linear_symmetries], _Clairaut]
\[ \boxed {y^{\prime }-\frac {\sqrt {x^{2}+4 y}}{2}=-\frac {x}{2}} \] With initial conditions \begin {align*} [y \left (6\right ) = -9] \end {align*}
✓ Solution by Maple
Time used: 0.844 (sec). Leaf size: 17
dsolve([diff(y(x),x)=(-x+sqrt(x^2+4*y(x)))/2,y(6) = -9],y(x), singsol=all)
\begin{align*} y \left (x \right ) = 9-3 x y \left (x \right ) = -\frac {x^{2}}{4} \end{align*}
✓ Solution by Mathematica
Time used: 0.987 (sec). Leaf size: 10
DSolve[{y'[x]==(-x+Sqrt[x^2+4*y[x]])/2,{y[6]==-9}},y[x],x,IncludeSingularSolutions -> True]
\[ y(x)\to 9-3 x \]