Internal problem ID [11809]
Book: Differential equations and the calculus of variations by L. ElSGOLTS. MIR PUBLISHERS,
MOSCOW, Third printing 1977.
Section: Chapter 1, First-Order Differential Equations. Problems page 88
Problem number: Problem 18.
ODE order: 1.
ODE degree: 4.
CAS Maple gives this as type [_quadrature]
\[ \boxed {y-{y^{\prime }}^{4}+{y^{\prime }}^{3}=-2} \]
✓ Solution by Maple
Time used: 0.016 (sec). Leaf size: 327
dsolve(y(x)=diff(y(x),x)^4-diff(y(x),x)^3-2,y(x), singsol=all)
\begin{align*} y \left (x \right ) = -2 y \left (x \right ) = \frac {\left (27-192 c_{1} +192 x +24 \sqrt {64 c_{1}^{2}-128 c_{1} x +64 x^{2}-18 c_{1} +18 x}\right )^{\frac {8}{3}}+4 \left (27-192 c_{1} +192 x +24 \sqrt {64 c_{1}^{2}-128 c_{1} x +64 x^{2}-18 c_{1} +18 x}\right )^{\frac {7}{3}}-8165 \left (27-192 c_{1} +192 x +24 \sqrt {64 c_{1}^{2}-128 c_{1} x +64 x^{2}-18 c_{1} +18 x}\right )^{\frac {4}{3}}+1458 \left (27-192 c_{1} +192 x +24 \sqrt {64 c_{1}^{2}-128 c_{1} x +64 x^{2}-18 c_{1} +18 x}\right )^{\frac {2}{3}}+1327104 c_{1}^{2}-2654208 c_{1} x +1327104 x^{2}-373248 c_{1} +373248 x -165888 c_{1} \sqrt {64 c_{1}^{2}-128 c_{1} x +64 x^{2}-18 c_{1} +18 x}+165888 x \sqrt {64 c_{1}^{2}-128 c_{1} x +64 x^{2}-18 c_{1} +18 x}+2916 \left (27-192 c_{1} +192 x +24 \sqrt {64 c_{1}^{2}-128 c_{1} x +64 x^{2}-18 c_{1} +18 x}\right )^{\frac {1}{3}}+23328 \sqrt {64 c_{1}^{2}-128 c_{1} x +64 x^{2}-18 c_{1} +18 x}+19683}{4096 \left (27-192 c_{1} +192 x +24 \sqrt {64 c_{1}^{2}-128 c_{1} x +64 x^{2}-18 c_{1} +18 x}\right )^{\frac {4}{3}}} \end{align*}
✗ Solution by Mathematica
Time used: 0.0 (sec). Leaf size: 0
DSolve[y[x]==y'[x]^4-y'[x]^3-2,y[x],x,IncludeSingularSolutions -> True]
Timed out