Internal problem ID [10833]
Book: Differential equations and the calculus of variations by L. ElSGOLTS. MIR PUBLISHERS,
MOSCOW, Third printing 1977.
Section: Chapter 2, DIFFERENTIAL EQUATIONS OF THE SECOND ORDER AND HIGHER.
Problems page 172
Problem number: Problem 18.
ODE order: 2.
ODE degree: 1.
CAS Maple gives this as type [[_2nd_order, _missing_x], [_2nd_order, _reducible, _mu_x_y1]]
\[ \boxed {y^{\prime \prime }-3 \sqrt {y}=0} \] With initial conditions \begin {align*} [y \left (0\right ) = 1, y^{\prime }\left (0\right ) = 2] \end {align*}
✓ Solution by Maple
Time used: 0.078 (sec). Leaf size: 11
dsolve([diff(y(x),x$2)=3*sqrt(y(x)),y(0) = 1, D(y)(0) = 2],y(x), singsol=all)
\[ y \left (x \right ) = \frac {\left (x +2\right )^{4}}{16} \]
✓ Solution by Mathematica
Time used: 0.063 (sec). Leaf size: 14
DSolve[{y''[x]==3*Sqrt[y[x]],{y[0]==1,y'[0]==2}},y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to \frac {1}{16} (x+2)^4 \\ \end{align*}