71.8.42 problem 14 (b)

Internal problem ID [14476]
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 (b)
Date solved : Tuesday, January 28, 2025 at 06:41:37 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 (0\right )&=0 \end{align*}

✓ Solution by Maple

Time used: 0.059 (sec). Leaf size: 13

dsolve([diff(y(x),x)=(-x+sqrt(x^2+4*y(x)))/2,y(0) = 0],y(x), singsol=all)
 

\begin{align*} y &= 0 \\ y &= -\frac {x^{2}}{4} \\ \end{align*}

✓ Solution by Mathematica

Time used: 0.446 (sec). Leaf size: 6

DSolve[{D[y[x],x]==(-x+Sqrt[x^2+4*y[x]])/2,{y[0]==0}},y[x],x,IncludeSingularSolutions -> True]
 

\[ y(x)\to 0 \]