51.1.64 problem 64

Internal problem ID [10334]
Book : First order enumerated odes
Section : section 1
Problem number : 64
Date solved : Tuesday, September 30, 2025 at 07:22:02 PM
CAS classification : [[_homogeneous, `class C`], _dAlembert]

\begin{align*} y^{\prime }&=\left (\pi +x +7 y\right )^{{7}/{2}} \end{align*}

✓ Maple. Time used: 0.019 (sec). Leaf size: 33

ode:=diff(y(x),x) = (Pi+x+7*y(x))^(7/2); 
dsolve(ode,y(x), singsol=all);
 

\[ y = -\frac {x}{7}+\operatorname {RootOf}\left (-x +7 \int _{}^{\textit {\_Z}}\frac {1}{1+7 \left (\pi +7 \textit {\_a} \right )^{{7}/{2}}}d \textit {\_a} +c_1 \right ) \]

✓ Mathematica. Time used: 2.337 (sec). Leaf size: 20120

ode=D[y[x],x]==(Pi+x+7*y[x])^(7/2); 
ic={}; 
DSolve[{ode,ic},y[x],x,IncludeSingularSolutions->True]
 

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✗ Sympy

from sympy import * 
x = symbols("x") 
y = Function("y") 
ode = Eq(-(x + 7*y(x) + pi)**(7/2) + Derivative(y(x), x),0) 
ics = {} 
dsolve(ode,func=y(x),ics=ics)
 

Timed Out