29.14.19 problem 400

Internal problem ID [4998]
Book : Ordinary differential equations and their solutions. By George Moseley Murphy. 1960
Section : Various 14
Problem number : 400
Date solved : Monday, January 27, 2025 at 10:02:25 AM
CAS classification : [_separable]

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

✓ Solution by Maple

Time used: 0.003 (sec). Leaf size: 28

dsolve(diff(y(x),x)*sqrt(x^3+1) = sqrt(1+y(x)^3),y(x), singsol=all)
 

\[ \int \frac {1}{\sqrt {x^{3}+1}}d x -\int _{}^{y \left (x \right )}\frac {1}{\sqrt {\textit {\_a}^{3}+1}}d \textit {\_a} +c_{1} = 0 \]

✓ Solution by Mathematica

Time used: 0.397 (sec). Leaf size: 71

DSolve[D[y[x],x] Sqrt[1+x^3]==Sqrt[1+y[x]^3],y[x],x,IncludeSingularSolutions -> True]
 

\begin{align*} y(x)\to \text {InverseFunction}\left [\text {$\#$1} \operatorname {Hypergeometric2F1}\left (\frac {1}{3},\frac {1}{2},\frac {4}{3},-\text {$\#$1}^3\right )\&\right ]\left [x \operatorname {Hypergeometric2F1}\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*}