81.1.20 problem 2-18

Internal problem ID [21465]
Book : The Differential Equations Problem Solver. VOL. I. M. Fogiel director. REA, NY. 1978. ISBN 78-63609
Section : Chapter 2. Separable differential equations
Problem number : 2-18
Date solved : Thursday, October 02, 2025 at 07:38:57 PM
CAS classification : [_separable]

\begin{align*} x \cos \left (x \right )+\left (1-6 y^{5}\right ) y^{\prime }&=0 \end{align*}

With initial conditions

\begin{align*} y \left (\pi \right )&=0 \\ \end{align*}

✓ Maple. Time used: 0.184 (sec). Leaf size: 22

ode:=x*cos(x)+(1-6*y(x)^5)*diff(y(x),x) = 0; 
ic:=[y(Pi) = 0]; 
dsolve([ode,op(ic)],y(x), singsol=all);
 

\[ y = \operatorname {RootOf}\left (\textit {\_Z}^{6}-x \sin \left (x \right )-\cos \left (x \right )-\textit {\_Z} -1\right ) \]

✓ Mathematica. Time used: 7.36 (sec). Leaf size: 27

ode=x*Cos[x]+(1-6*y[x]^5)*D[y[x],x]==0; 
ic={y[Pi]==0}; 
DSolve[{ode,ic},y[x],x,IncludeSingularSolutions->True]
 

\begin{align*} y(x)&\to \text {Root}\left [\text {$\#$1}^6-\text {$\#$1}-x \sin (x)-\cos (x)-1\&,1\right ] \end{align*}

✓ Sympy. Time used: 0.139 (sec). Leaf size: 17

from sympy import * 
x = symbols("x") 
y = Function("y") 
ode = Eq(x*cos(x) + (1 - 6*y(x)**5)*Derivative(y(x), x),0) 
ics = {y(pi): 0} 
dsolve(ode,func=y(x),ics=ics)
 

\[ - x \sin {\left (x \right )} + y^{6}{\left (x \right )} - y{\left (x \right )} - \cos {\left (x \right )} = 1 \]