71.8.41 problem 14 (a)

Internal problem ID [14475]
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 (a)
Date solved : Tuesday, January 28, 2025 at 06:41:34 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 )&=1 \end{align*}

✓ Solution by Maple

Time used: 1.500 (sec). Leaf size: 15

dsolve([diff(y(x),x)=(-x+sqrt(x^2+4*y(x)))/2,y(0) = 1],y(x), singsol=all)
 

\begin{align*} y &= 1-x \\ y &= x +1 \\ \end{align*}

✓ Solution by Mathematica

Time used: 0.533 (sec). Leaf size: 17

DSolve[{D[y[x],x]==(-x+Sqrt[x^2+4*y[x]])/2,{y[0]==1}},y[x],x,IncludeSingularSolutions -> True]
 

\begin{align*} y(x)\to 1-x \\ y(x)\to x+1 \\ \end{align*}