69.1.76 problem 121

Internal problem ID [14229]
Book : DIFFERENTIAL and INTEGRAL CALCULUS. VOL I. by N. PISKUNOV. MIR PUBLISHERS, Moscow 1969.
Section : Chapter 8. Differential equations. Exercises page 595
Problem number : 121
Date solved : Tuesday, January 28, 2025 at 06:22:43 AM
CAS classification : [[_2nd_order, _missing_x], [_2nd_order, _reducible, _mu_x_y1]]

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

✓ Solution by Maple

Time used: 0.079 (sec). Leaf size: 46

dsolve(diff(y(x),x$2)=a/y(x)^3,y(x), singsol=all)
 

\begin{align*} y &= \frac {\sqrt {c_{1} \left (\left (x +c_{2} \right )^{2} c_{1}^{2}+a \right )}}{c_{1}} \\ y &= -\frac {\sqrt {c_{1} \left (\left (x +c_{2} \right )^{2} c_{1}^{2}+a \right )}}{c_{1}} \\ \end{align*}

✓ Solution by Mathematica

Time used: 2.925 (sec). Leaf size: 63

DSolve[D[y[x],{x,2}]==a/y[x]^3,y[x],x,IncludeSingularSolutions -> True]
 

\begin{align*} y(x)\to -\frac {\sqrt {a+c_1{}^2 (x+c_2){}^2}}{\sqrt {c_1}} \\ y(x)\to \frac {\sqrt {a+c_1{}^2 (x+c_2){}^2}}{\sqrt {c_1}} \\ y(x)\to \text {Indeterminate} \\ \end{align*}