84.8.8 problem 4.17

Internal problem ID [22120]
Book : Schaums outline series. Differential Equations By Richard Bronson. 1973. McGraw-Hill Inc. ISBN 0-07-008009-7
Section : Chapter 4. Separable first-order differential equations. Supplementary problems
Problem number : 4.17
Date solved : Thursday, October 02, 2025 at 08:25:31 PM
CAS classification : [_separable]

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

With initial conditions

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

✓ Maple. Time used: 0.056 (sec). Leaf size: 22

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

\[ y = \operatorname {RootOf}\left (\textit {\_Z}^{6}+6 x \,{\mathrm e}^{x}-6 \textit {\_Z} -6 \,{\mathrm e}^{x}+6\right ) \]

✓ Mathematica. Time used: 6.145 (sec). Leaf size: 29

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

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

✓ Sympy. Time used: 0.129 (sec). Leaf size: 19

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

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