Internal problem ID [3802]
Book: Ordinary differential equations and their solutions. By George Moseley Murphy.
1960
Section: Various 36
Problem number: 1098.
ODE order: 1.
ODE degree: 5.
CAS Maple gives this as type [_quadrature]
Solve \begin {gather*} \boxed {3 \left (y^{\prime }\right )^{5}-y y^{\prime }+1=0} \end {gather*}
✓ Solution by Maple
Time used: 0.133 (sec). Leaf size: 87
dsolve(3*diff(y(x),x)^5-y(x)*diff(y(x),x)+1 = 0,y(x), singsol=all)
\[ y \relax (x ) = \frac {5 \RootOf \left (1+8 \textit {\_Z}^{5}+\left (-2 x +2 c_{1}\right ) \textit {\_Z}^{2}\right )^{3}+2 c_{1}-2 x}{2 \RootOf \left (1+8 \textit {\_Z}^{5}+\left (-2 x +2 c_{1}\right ) \textit {\_Z}^{2}\right ) \left (4 \RootOf \left (1+8 \textit {\_Z}^{5}+\left (-2 x +2 c_{1}\right ) \textit {\_Z}^{2}\right )^{3}+c_{1}-x \right )} \]
✓ Solution by Mathematica
Time used: 0.124 (sec). Leaf size: 176
DSolve[3 (y'[x])^5 -y[x] y'[x]+1==0,y[x],x,IncludeSingularSolutions -> True]
\begin{align*} \text {Solve}\left [\int _1^{y(x)}\frac {1}{\text {Root}\left [3 \text {$\#$1}^5-K[1] \text {$\#$1}+1\&,1\right ]}dK[1]=x+c_1,y(x)\right ] \\ \text {Solve}\left [\int _1^{y(x)}\frac {1}{\text {Root}\left [3 \text {$\#$1}^5-K[2] \text {$\#$1}+1\&,2\right ]}dK[2]=x+c_1,y(x)\right ] \\ \text {Solve}\left [\int _1^{y(x)}\frac {1}{\text {Root}\left [3 \text {$\#$1}^5-K[3] \text {$\#$1}+1\&,3\right ]}dK[3]=x+c_1,y(x)\right ] \\ \text {Solve}\left [\int _1^{y(x)}\frac {1}{\text {Root}\left [3 \text {$\#$1}^5-K[4] \text {$\#$1}+1\&,4\right ]}dK[4]=x+c_1,y(x)\right ] \\ \text {Solve}\left [\int _1^{y(x)}\frac {1}{\text {Root}\left [3 \text {$\#$1}^5-K[5] \text {$\#$1}+1\&,5\right ]}dK[5]=x+c_1,y(x)\right ] \\ \end{align*}