34.23 problem 1025

Internal problem ID [3742]

Book: Ordinary differential equations and their solutions. By George Moseley Murphy. 1960
Section: Various 34
Problem number: 1025.
ODE order: 1.
ODE degree: 3.

CAS Maple gives this as type [_quadrature]

Solve \begin {gather*} \boxed {\left (y^{\prime }\right )^{3}-7 y^{\prime }+6=0} \end {gather*}

Solution by Maple

Time used: 0.002 (sec). Leaf size: 23

dsolve(diff(y(x),x)^3-7*diff(y(x),x)+6 = 0,y(x), singsol=all)
 

\begin{align*} y \relax (x ) = 2 x +c_{1} \\ y \relax (x ) = c_{1}+x \\ y \relax (x ) = -3 x +c_{1} \\ \end{align*}

Solution by Mathematica

Time used: 0.003 (sec). Leaf size: 29

DSolve[(y'[x])^3-7 y'[x]+6==0,y[x],x,IncludeSingularSolutions -> True]
 

\begin{align*} y(x)\to -3 x+c_1 \\ y(x)\to x+c_1 \\ y(x)\to 2 x+c_1 \\ \end{align*}