57.1.63 problem 63

Internal problem ID [9047]
Book : First order enumerated odes
Section : section 1
Problem number : 63
Date solved : Sunday, March 30, 2025 at 02:00:19 PM
CAS classification : [[_homogeneous, `class C`], _dAlembert]

\begin{align*} y^{\prime }&=\left (a +b x +y\right )^{4} \end{align*}

✓ Maple. Time used: 0.011 (sec). Leaf size: 49

ode:=diff(y(x),x) = (a+b*x+y(x))^4; 
dsolve(ode,y(x), singsol=all);
 

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

✓ Mathematica. Time used: 0.423 (sec). Leaf size: 163

ode=D[y[x],x]==(a+b*x+y[x])^(4); 
ic={}; 
DSolve[{ode,ic},y[x],x,IncludeSingularSolutions->True]
 

\[ \text {Solve}\left [\frac {2 \sqrt {2} \arctan \left (1-\frac {\sqrt {2} (a+b x+y(x))}{\sqrt [4]{b}}\right )-2 \sqrt {2} \arctan \left (\frac {\sqrt {2} (a+b x+y(x))}{\sqrt [4]{b}}+1\right )+\sqrt {2} \log \left ((a+b x+y(x))^2-\sqrt {2} \sqrt [4]{b} (a+b x+y(x))+\sqrt {b}\right )-\sqrt {2} \log \left ((a+b x+y(x))^2+\sqrt {2} \sqrt [4]{b} (a+b x+y(x))+\sqrt {b}\right )+8 b^{3/4} x}{8 b^{3/4}}=c_1,y(x)\right ] \]

✗ Sympy

from sympy import * 
x = symbols("x") 
a = symbols("a") 
b = symbols("b") 
y = Function("y") 
ode = Eq(-(a + b*x + y(x))**4 + Derivative(y(x), x),0) 
ics = {} 
dsolve(ode,func=y(x),ics=ics)
 

TypeError : argument of type Mul is not iterable