15.22.1 problem 1

Internal problem ID [3335]
Book : Differential Equations by Alfred L. Nelson, Karl W. Folley, Max Coral. 3rd ed. DC heath. Boston. 1964
Section : Exercise 40, page 186
Problem number : 1
Date solved : Monday, January 27, 2025 at 07:34:28 AM
CAS classification : [_quadrature]

\begin{align*} y^{\prime }&=\sqrt {1-y} \end{align*}

Using series method with expansion around

\begin{align*} 0 \end{align*}

With initial conditions

\begin{align*} y \left (0\right )&=0 \end{align*}

✓ Solution by Maple

Time used: 0.003 (sec). Leaf size: 11

Order:=5; 
dsolve([diff(y(x),x)=(1-y(x))^(1/2),y(0) = 0],y(x),type='series',x=0);
 

\[ y \left (x \right ) = x -\frac {1}{4} x^{2} \]

✓ Solution by Mathematica

Time used: 0.098 (sec). Leaf size: 12

AsymptoticDSolveValue[{D[y[x],x]==(1-y[x])^(1/2),{y[0]==0}},y[x],{x,0,"5"-1}]
 

\[ y(x)\to x-\frac {x^2}{4} \]