Internal problem ID [2364]
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.
ODE order: 1.
ODE degree: 1.
CAS Maple gives this as type [_quadrature]
\[ \boxed {y^{\prime }-\sqrt {1-y}=0} \] With initial conditions \begin {align*} [y \left (0\right ) = 0] \end {align*}
With the expansion point for the power series method at \(x = 0\).
✓ Solution by Maple
Time used: 0.0 (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: 0.032 (sec). Leaf size: 12
AsymptoticDSolveValue[{y'[x]==(1-y[x])^(1/2),{y[0]==0}},y[x],{x,0,4}]
\[ y(x)\to x-\frac {x^2}{4} \]