Internal problem ID [3800]
Book: Ordinary differential equations and their solutions. By George Moseley Murphy.
1960
Section: Various 36
Problem number: 1094.
ODE order: 1.
ODE degree: 4.
CAS Maple gives this as type [_quadrature]
Solve \begin {gather*} \boxed {2 \left (y^{\prime }\right )^{4}-y y^{\prime }-2=0} \end {gather*}
✓ Solution by Maple
Time used: 0.149 (sec). Leaf size: 513
dsolve(2*diff(y(x),x)^4-y(x)*diff(y(x),x)-2 = 0,y(x), singsol=all)
\begin{align*} y \relax (x ) = -\frac {\sqrt {-6 c_{1}^{3}+18 c_{1}^{2} x -18 c_{1} x^{2}+6 x^{3}+216 c_{1}-216 x -6 \sqrt {c_{1}^{6}-6 c_{1}^{5} x +15 c_{1}^{4} x^{2}-20 x^{3} c_{1}^{3}+15 c_{1}^{2} x^{4}-6 c_{1} x^{5}+x^{6}+36 c_{1}^{4}-144 c_{1}^{3} x +216 c_{1}^{2} x^{2}-144 x^{3} c_{1}+36 x^{4}+432 c_{1}^{2}-864 c_{1} x +432 x^{2}+1728}}}{9} \\ y \relax (x ) = \frac {\sqrt {-6 c_{1}^{3}+18 c_{1}^{2} x -18 c_{1} x^{2}+6 x^{3}+216 c_{1}-216 x -6 \sqrt {c_{1}^{6}-6 c_{1}^{5} x +15 c_{1}^{4} x^{2}-20 x^{3} c_{1}^{3}+15 c_{1}^{2} x^{4}-6 c_{1} x^{5}+x^{6}+36 c_{1}^{4}-144 c_{1}^{3} x +216 c_{1}^{2} x^{2}-144 x^{3} c_{1}+36 x^{4}+432 c_{1}^{2}-864 c_{1} x +432 x^{2}+1728}}}{9} \\ y \relax (x ) = -\frac {\sqrt {-6 c_{1}^{3}+18 c_{1}^{2} x -18 c_{1} x^{2}+6 x^{3}+216 c_{1}-216 x +6 \sqrt {c_{1}^{6}-6 c_{1}^{5} x +15 c_{1}^{4} x^{2}-20 x^{3} c_{1}^{3}+15 c_{1}^{2} x^{4}-6 c_{1} x^{5}+x^{6}+36 c_{1}^{4}-144 c_{1}^{3} x +216 c_{1}^{2} x^{2}-144 x^{3} c_{1}+36 x^{4}+432 c_{1}^{2}-864 c_{1} x +432 x^{2}+1728}}}{9} \\ y \relax (x ) = \frac {\sqrt {-6 c_{1}^{3}+18 c_{1}^{2} x -18 c_{1} x^{2}+6 x^{3}+216 c_{1}-216 x +6 \sqrt {c_{1}^{6}-6 c_{1}^{5} x +15 c_{1}^{4} x^{2}-20 x^{3} c_{1}^{3}+15 c_{1}^{2} x^{4}-6 c_{1} x^{5}+x^{6}+36 c_{1}^{4}-144 c_{1}^{3} x +216 c_{1}^{2} x^{2}-144 x^{3} c_{1}+36 x^{4}+432 c_{1}^{2}-864 c_{1} x +432 x^{2}+1728}}}{9} \\ \end{align*}
✓ Solution by Mathematica
Time used: 151.176 (sec). Leaf size: 12753
DSolve[2 (y'[x])^4 -y[x] y'[x]-2 ==0,y[x],x,IncludeSingularSolutions -> True]
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