Internal problem ID [2371]
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: 8.
ODE order: 1.
ODE degree: 1.
CAS Maple gives this as type [`y=_G(x,y')`]
\[ \boxed {y^{\prime }-\sqrt {1+y x}=0} \] With initial conditions \begin {align*} [y \left (0\right ) = 1] \end {align*}
With the expansion point for the power series method at \(x = 0\).
✓ Solution by Maple
Time used: 0.015 (sec). Leaf size: 16
Order:=4; dsolve([diff(y(x),x)=sqrt(1+x*y(x)),y(0) = 1],y(x),type='series',x=0);
\[ y \left (x \right ) = 1+x +\frac {1}{4} x^{2}+\frac {1}{8} x^{3}+\operatorname {O}\left (x^{4}\right ) \]
✗ Solution by Mathematica
Time used: 0.0 (sec). Leaf size: 0
AsymptoticDSolveValue[{y'[x]==Sqrt[1+x*y[x]],{y[0]==1}},y[x],{x,0,3}]
Not solved