51.1.65 problem 65

Internal problem ID [10335]
Book : First order enumerated odes
Section : section 1
Problem number : 65
Date solved : Tuesday, September 30, 2025 at 07:22:10 PM
CAS classification : [[_homogeneous, `class C`], _dAlembert]

\begin{align*} y^{\prime }&=\left (a +b x +c y\right )^{6} \end{align*}

✓ Maple. Time used: 0.014 (sec). Leaf size: 94

ode:=diff(y(x),x) = (a+b*x+c*y(x))^6; 
dsolve(ode,y(x), singsol=all);
 

\[ y = \frac {\operatorname {RootOf}\left (\int _{}^{\textit {\_Z}}\frac {1}{c^{7} \textit {\_a}^{6}+6 \textit {\_a}^{5} a \,c^{6}+15 \textit {\_a}^{4} a^{2} c^{5}+20 \textit {\_a}^{3} a^{3} c^{4}+15 \textit {\_a}^{2} a^{4} c^{3}+6 \textit {\_a} \,a^{5} c^{2}+a^{6} c +b}d \textit {\_a} c -x +c_1 \right ) c -b x}{c} \]

✓ Mathematica. Time used: 0.684 (sec). Leaf size: 1416

ode=D[y[x],x]==(a+b*x+c*y[x])^6; 
ic={}; 
DSolve[{ode,ic},y[x],x,IncludeSingularSolutions->True]
 

\begin{align*} \text {Solution too large to show}\end{align*}

✗ Sympy

from sympy import * 
x = symbols("x") 
a = symbols("a") 
b = symbols("b") 
c = symbols("c") 
y = Function("y") 
ode = Eq(-(a + b*x + c*y(x))**6 + Derivative(y(x), x),0) 
ics = {} 
dsolve(ode,func=y(x),ics=ics)
 

TypeError : argument of type Mul is not iterable