Internal problem ID [5345]
Book: An introduction to Ordinary Differential Equations. Earl A. Coddington. Dover. NY
1961
Section: Chapter 6. Existence and uniqueness of solutions to systems and nth order equations. Page
238
Problem number: 3.
ODE order: 2.
ODE degree: 1.
CAS Maple gives this as type [[_2nd_order, _missing_x], [_2nd_order, _reducible, _mu_poly_yn]]
Solve \begin {gather*} \boxed {y^{\prime \prime }+\frac {1}{2 \left (y^{\prime }\right )^{2}}=0} \end {gather*} With initial conditions \begin {align*} [y \relax (0) = 1, y^{\prime }\relax (0) = -1] \end {align*}
✓ Solution by Maple
Time used: 0.563 (sec). Leaf size: 26
dsolve([diff(y(x),x$2)=-1/(2*diff(y(x),x)^2),y(0) = 1, D(y)(0) = -1],y(x), singsol=all)
\[ y \relax (x ) = \frac {3 \left (x +\frac {2}{3}\right ) \left (-12 x -8\right )^{\frac {1}{3}} \left (-1+i \sqrt {3}\right )}{16}+\frac {3}{2} \]
✓ Solution by Mathematica
Time used: 0.019 (sec). Leaf size: 27
DSolve[{y''[x]==-1/(2*(y'[x])^2),{y[0]==1,y'[0]==-1}},y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to \frac {1}{8} \left (12-(-2)^{2/3} (-3 x-2)^{4/3}\right ) \\ \end{align*}