71.4.24 problem 24

Internal problem ID [14396]
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
Date solved : Tuesday, January 28, 2025 at 06:29:40 AM
CAS classification : [[_1st_order, _with_linear_symmetries], _Clairaut]

\begin{align*} y^{\prime }&=-\frac {x}{2}+\frac {\sqrt {x^{2}+4 y}}{2} \end{align*}

With initial conditions

\begin{align*} y \left (6\right )&=-9 \end{align*}

✓ Solution by Maple

Time used: 2.775 (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 &= -3 x +9 \\ y &= -\frac {x^{2}}{4} \\ \end{align*}

✓ Solution by Mathematica

Time used: 0.783 (sec). Leaf size: 10

DSolve[{D[y[x],x]==(-x+Sqrt[x^2+4*y[x]])/2,{y[6]==-9}},y[x],x,IncludeSingularSolutions -> True]
 

\[ y(x)\to 9-3 x \]