Internal problem ID [2377]
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: 14.
ODE order: 2.
ODE degree: 1.
CAS Maple gives this as type [[_2nd_order, _missing_x]]
\[ \boxed {y^{\prime \prime }+\frac {{y^{\prime }}^{2}}{2}-y=0} \] With initial conditions \begin {align*} [y \left (0\right ) = 0, y^{\prime }\left (0\right ) = 1] \end {align*}
With the expansion point for the power series method at \(x = 0\).
✓ Solution by Maple
Time used: 0.0 (sec). Leaf size: 20
Order:=7; dsolve([diff(y(x),x$2)+1/2*diff(y(x),x)^2-y(x)=0,y(0) = 0, D(y)(0) = 1],y(x),type='series',x=0);
\[ y \left (x \right ) = x -\frac {1}{4} x^{2}+\frac {1}{4} x^{3}-\frac {3}{32} x^{4}+\frac {1}{20} x^{5}-\frac {13}{480} x^{6}+\operatorname {O}\left (x^{7}\right ) \]
✗ Solution by Mathematica
Time used: 0.0 (sec). Leaf size: 0
AsymptoticDSolveValue[{y''[x]+1/2*y'[x]^2-y[x]==0,{y[0]==0,y'[0]==1}},y[x],{x,0,6}]
Not solved