15.18.31 problem 31

Internal problem ID [3274]
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
Date solved : Monday, January 27, 2025 at 07:30:24 AM
CAS classification : [[_2nd_order, _missing_x], [_2nd_order, _reducible, _mu_x_y1]]

\begin{align*} y^{\prime \prime }&=y^{3} \end{align*}

With initial conditions

\begin{align*} y \left (0\right )&=-1\\ y^{\prime }\left (0\right )&=\frac {\sqrt {2}}{2} \end{align*}

✓ Solution by Maple

Time used: 0.071 (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: 0.040 (sec). Leaf size: 18

DSolve[{D[y[x],{x,2}]==y[x]^3,{y[0]==1,Derivative[1][y][0] ==Sqrt[2]/2}},y[x],x,IncludeSingularSolutions -> True]
 

\[ y(x)\to -\frac {2}{\sqrt {2} x-2} \]