Internal problem ID [4308]
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]
\[ \boxed {2 {y^{\prime }}^{4}-y y^{\prime }=2} \]
✓ Solution by Maple
Time used: 0.031 (sec). Leaf size: 217
dsolve(2*diff(y(x),x)^4-y(x)*diff(y(x),x)-2 = 0,y(x), singsol=all)
\begin{align*} y \left (x \right ) &= -\frac {\sqrt {-6 \sqrt {\left (c_{1}^{2}-2 c_{1} x +x^{2}+12\right )^{3}}-6 c_{1}^{3}+18 c_{1}^{2} x +\left (-18 x^{2}+216\right ) c_{1} +6 x^{3}-216 x}}{9} \\ y \left (x \right ) &= \frac {\sqrt {-6 \sqrt {\left (c_{1}^{2}-2 c_{1} x +x^{2}+12\right )^{3}}-6 c_{1}^{3}+18 c_{1}^{2} x +\left (-18 x^{2}+216\right ) c_{1} +6 x^{3}-216 x}}{9} \\ y \left (x \right ) &= -\frac {\sqrt {6 \sqrt {\left (c_{1}^{2}-2 c_{1} x +x^{2}+12\right )^{3}}-6 c_{1}^{3}+18 c_{1}^{2} x +\left (-18 x^{2}+216\right ) c_{1} +6 x^{3}-216 x}}{9} \\ y \left (x \right ) &= \frac {\sqrt {6 \sqrt {\left (c_{1}^{2}-2 c_{1} x +x^{2}+12\right )^{3}}-6 c_{1}^{3}+18 c_{1}^{2} x +\left (-18 x^{2}+216\right ) c_{1} +6 x^{3}-216 x}}{9} \\ \end{align*}
✓ Solution by Mathematica
Time used: 116.271 (sec). Leaf size: 12753
DSolve[2 (y'[x])^4 -y[x] y'[x]-2 ==0,y[x],x,IncludeSingularSolutions -> True]
Too large to display