Internal problem ID [12743]
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 (e).
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*} \left [y \left (1\right ) = -{\frac {1}{4}}\right ] \end {align*}
✓ Solution by Maple
Time used: 8.516 (sec). Leaf size: 17
dsolve([diff(y(x),x)=(-x+sqrt(x^2+4*y(x)))/2,y(1) = -1/4],y(x), singsol=all)
\begin{align*} y \left (x \right ) &= -\frac {x^{2}}{4} \\ y \left (x \right ) &= \frac {1}{4}-\frac {x}{2} \\ \end{align*}
✓ Solution by Mathematica
Time used: 0.282 (sec). Leaf size: 14
DSolve[{y'[x]==(-x+Sqrt[x^2+4*y[x]])/2,{y[1]==-1/4}},y[x],x,IncludeSingularSolutions -> True]
\[ y(x)\to \frac {1}{4} (1-2 x) \]