7.5.52 problem 52

Internal problem ID [156]
Book : Elementary Differential Equations. By C. Henry Edwards, David E. Penney and David Calvis. 6th edition. 2008
Section : Chapter 1. First order differential equations. Section 1.6 (substitution and exact equations). Problems at page 72
Problem number : 52
Date solved : Friday, February 07, 2025 at 07:58:55 AM
CAS classification : [[_2nd_order, _missing_x], [_2nd_order, _reducible, _mu_x_y1]]

\begin{align*} y^{3} y^{\prime \prime }&=1 \end{align*}

✓ Solution by Maple

Time used: 0.029 (sec). Leaf size: 46

dsolve(y(x)^3*diff(y(x),x$2)=1,y(x), singsol=all)
 

\begin{align*} y &= \frac {\sqrt {c_1 \left (1+\left (x +c_2 \right )^{2} c_1^{2}\right )}}{c_1} \\ y &= -\frac {\sqrt {c_1 \left (1+\left (x +c_2 \right )^{2} c_1^{2}\right )}}{c_1} \\ \end{align*}

✓ Solution by Mathematica

Time used: 3.387 (sec). Leaf size: 93

DSolve[y[x]^3*D[y[x],{x,2}]==1,y[x],x,IncludeSingularSolutions -> True]
 

\begin{align*} y(x)\to -\frac {\sqrt {c_1{}^2 x^2+2 c_2 c_1{}^2 x+1+c_2{}^2 c_1{}^2}}{\sqrt {c_1}} \\ y(x)\to \frac {\sqrt {c_1{}^2 x^2+2 c_2 c_1{}^2 x+1+c_2{}^2 c_1{}^2}}{\sqrt {c_1}} \\ y(x)\to \text {Indeterminate} \\ \end{align*}