Internal problem ID [12421]
Book: Ordinary Differential Equations by Charles E. Roberts, Jr. CRC Press. 2010
Section: Chapter 2. The Initial Value Problem. Exercises 2.4.4, page 115
Problem number: 14 (c).
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 (0\right ) = -1] \end {align*}
✓ Solution by Maple
Time used: 0.156 (sec). Leaf size: 19
dsolve([diff(y(x),x)=(-x+sqrt(x^2+4*y(x)))/2,y(0) = -1],y(x), singsol=all)
\begin{align*} y \left (x \right ) = -i x -1 y \left (x \right ) = i x -1 \end{align*}
✓ Solution by Mathematica
Time used: 0.293 (sec). Leaf size: 23
DSolve[{y'[x]==(-x+Sqrt[x^2+4*y[x]])/2,{y[0]==-1}},y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to -1-i x y(x)\to -1+i x \end{align*}