Internal problem ID [12422]
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 (d).
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}{5}}\right ] \end {align*}
✓ Solution by Maple
Time used: 0.515 (sec). Leaf size: 69
dsolve([diff(y(x),x)=(-x+sqrt(x^2+4*y(x)))/2,y(1) = -1/5],y(x), singsol=all)
\begin{align*} y \left (x \right ) = \frac {\left (x -1\right ) \sqrt {5}}{10}-\frac {x}{2}+\frac {3}{10} y \left (x \right ) = \frac {\left (-5+\sqrt {5}\right ) \left (\sqrt {5}-5+10 x \right )}{100} y \left (x \right ) = -\frac {2^{\frac {1}{3}} \left (2^{\frac {1}{3}} x -\frac {\left (50+20 \sqrt {5}\right )^{\frac {1}{3}}}{5}\right ) \left (50+20 \sqrt {5}\right )^{\frac {1}{3}}}{10} \end{align*}
✓ Solution by Mathematica
Time used: 0.301 (sec). Leaf size: 51
DSolve[{y'[x]==(-x+Sqrt[x^2+4*y[x]])/2,{y[1]==-2/10}},y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to \frac {1}{100} \left (5+\sqrt {5}\right ) \left (-10 x+\sqrt {5}+5\right ) y(x)\to \frac {1}{100} \left (\sqrt {5}-5\right ) \left (10 x+\sqrt {5}-5\right ) \end{align*}