Internal problem ID [15180]
Book: A book of problems in ordinary differential equations. M.L. KRASNOV, A.L. KISELYOV,
G.I. MARKARENKO. MIR, MOSCOW. 1983
Section: Chapter 2 (Higher order ODE’s). Section 13. Basic concepts and definitions. Exercises
page 98
Problem number: 322.
ODE order: 1.
ODE degree: 4.
CAS Maple gives this as type [_quadrature]
\[ \boxed {{y^{\prime }}^{4}=1} \]
✓ Solution by Maple
Time used: 0.016 (sec). Leaf size: 33
dsolve(diff(y(x),x)*diff(y(x),x)^3=1,y(x), singsol=all)
\begin{align*} y &= -i x +c_{1} \\ y &= i x +c_{1} \\ y &= x +c_{1} \\ y &= -x +c_{1} \\ \end{align*}
✓ Solution by Mathematica
Time used: 0.003 (sec). Leaf size: 43
DSolve[y'[x]*y'[x]^3==1,y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to -x+c_1 \\ y(x)\to c_1-i x \\ y(x)\to i x+c_1 \\ y(x)\to x+c_1 \\ \end{align*}