83.29.2 problem 2

Internal problem ID [19375]
Book : A Text book for differentional equations for postgraduate students by Ray and Chaturvedi. First edition, 1958. BHASKAR press. INDIA
Section : Chapter VII. Exact differential equations and certain particular forms of equations. Exercise VII (C) at page 107
Problem number : 2
Date solved : Tuesday, January 28, 2025 at 01:35:46 PM
CAS classification : [[_2nd_order, _missing_x], [_2nd_order, _reducible, _mu_x_y1]]

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

✓ Solution by Maple

Time used: 0.040 (sec). Leaf size: 46

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

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

✓ Solution by Mathematica

Time used: 2.746 (sec). Leaf size: 63

DSolve[y[x]^3*D[y[x],{x,2}]==a,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*}