Internal problem ID [2303]
Book: Differential Equations by Alfred L. Nelson, Karl W. Folley, Max Coral. 3rd ed. DC heath.
Boston. 1964
Section: Exercise 35, page 157
Problem number: 31.
ODE order: 2.
ODE degree: 1.
CAS Maple gives this as type [[_2nd_order, _missing_x], [_2nd_order, _reducible, _mu_x_y1]]
\[ \boxed {y^{\prime \prime }-y^{3}=0} \] With initial conditions \begin {align*} \left [y \left (0\right ) = -1, y^{\prime }\left (0\right ) = \frac {\sqrt {2}}{2}\right ] \end {align*}
✓ Solution by Maple
Time used: 0.094 (sec). Leaf size: 16
dsolve([diff(y(x),x$2)=y(x)^3,y(0) = -1, D(y)(0) = 1/2*2^(1/2)],y(x), singsol=all)
\[ y \left (x \right ) = -\frac {\sqrt {2}}{x +\sqrt {2}} \]
✓ Solution by Mathematica
Time used: 0.038 (sec). Leaf size: 18
DSolve[{y''[x]==y[x]^3,{y[0]==1,y'[0]==Sqrt[2]/2}},y[x],x,IncludeSingularSolutions -> True]
\[ y(x)\to -\frac {2}{\sqrt {2} x-2} \]