Internal problem ID [3153]
Book: Ordinary differential equations and their solutions. By George Moseley Murphy.
1960
Section: Various 14
Problem number: 407.
ODE order: 1.
ODE degree: 1.
CAS Maple gives this as type [_separable]
Solve \begin {gather*} \boxed {y^{\prime } \left (x^{3}+1\right )^{\frac {2}{3}}+\left (1+y^{3}\right )^{\frac {2}{3}}=0} \end {gather*}
✓ Solution by Maple
Time used: 0.016 (sec). Leaf size: 33
dsolve(diff(y(x),x)*(x^3+1)^(2/3)+(1+y(x)^3)^(2/3) = 0,y(x), singsol=all)
\[ x \hypergeom \left (\left [\frac {1}{3}, \frac {2}{3}\right ], \left [\frac {4}{3}\right ], -x^{3}\right )+y \relax (x ) \hypergeom \left (\left [\frac {1}{3}, \frac {2}{3}\right ], \left [\frac {4}{3}\right ], -y \relax (x )^{3}\right )+c_{1} = 0 \]
✓ Solution by Mathematica
Time used: 2.846 (sec). Leaf size: 221
DSolve[y'[x](1+x^3)^(2/3)+(1+y[x]^3)^(2/3)==0,y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to \text {InverseFunction}\left [\frac {3 \sqrt [3]{\frac {\sqrt [3]{-1}-\text {$\#$1}}{1+\sqrt [3]{-1}}} (\text {$\#$1}+1) \left (\frac {\text {$\#$1}+(-1)^{2/3}}{(-1)^{2/3}-1}\right )^{2/3} \, _2F_1\left (\frac {1}{3},\frac {2}{3};\frac {4}{3};\frac {\sqrt [3]{-1} (\text {$\#$1}+1)}{\left (-1+\sqrt [3]{-1}\right ) \text {$\#$1}+1}\right )}{\left (\text {$\#$1}^3+1\right )^{2/3}}\&\right ]\left [-\frac {3 \sqrt [3]{\frac {\sqrt [3]{-1}-x}{1+\sqrt [3]{-1}}} (x+1) \left (\frac {x+(-1)^{2/3}}{(-1)^{2/3}-1}\right )^{2/3} \, _2F_1\left (\frac {1}{3},\frac {2}{3};\frac {4}{3};\frac {\sqrt [3]{-1} (x+1)}{\left (-1+\sqrt [3]{-1}\right ) x+1}\right )}{\left (x^3+1\right )^{2/3}}+c_1\right ] \\ y(x)\to -1 \\ y(x)\to \sqrt [3]{-1} \\ y(x)\to -(-1)^{2/3} \\ \end{align*}