Internal problem ID [3146]
Book: Ordinary differential equations and their solutions. By George Moseley Murphy.
1960
Section: Various 14
Problem number: 400.
ODE order: 1.
ODE degree: 1.
CAS Maple gives this as type [_separable]
Solve \begin {gather*} \boxed {y^{\prime } \sqrt {x^{3}+1}-\sqrt {1+y^{3}}=0} \end {gather*}
✓ Solution by Maple
Time used: 0.015 (sec). Leaf size: 28
dsolve(diff(y(x),x)*sqrt(x^3+1) = sqrt(1+y(x)^3),y(x), singsol=all)
\[ \int \frac {1}{\sqrt {x^{3}+1}}d x -\left (\int _{}^{y \relax (x )}\frac {1}{\sqrt {\textit {\_a}^{3}+1}}d \textit {\_a} \right )+c_{1} = 0 \]
✓ Solution by Mathematica
Time used: 40.428 (sec). Leaf size: 71
DSolve[y'[x] Sqrt[1+x^3]==Sqrt[1+y[x]^3],y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to \text {InverseFunction}\left [\text {$\#$1} \, _2F_1\left (\frac {1}{3},\frac {1}{2};\frac {4}{3};-\text {$\#$1}^3\right )\&\right ]\left [x \, _2F_1\left (\frac {1}{3},\frac {1}{2};\frac {4}{3};-x^3\right )+c_1\right ] \\ y(x)\to -1 \\ y(x)\to \sqrt [3]{-1} \\ y(x)\to -(-1)^{2/3} \\ \end{align*}