84.7.4 problem 4.4

Internal problem ID [22110]
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. Solved problems. Page 14
Problem number : 4.4
Date solved : Thursday, October 02, 2025 at 08:25:11 PM
CAS classification : [_separable]

\begin{align*} y^{\prime }&=\frac {1+x}{1+y^{4}} \end{align*}

✓ Maple. Time used: 0.002 (sec). Leaf size: 21

ode:=diff(y(x),x) = (1+x)/(y(x)^4+1); 
dsolve(ode,y(x), singsol=all);
 

\[ \frac {x^{2}}{2}+x -\frac {y^{5}}{5}-y+c_1 = 0 \]

✓ Mathematica. Time used: 3.319 (sec). Leaf size: 151

ode=D[y[x],x]==(x+1)/(y[x]^4+1); 
ic={}; 
DSolve[{ode,ic},y[x],x,IncludeSingularSolutions->True]
 

\begin{align*} y(x)&\to \text {Root}\left [2 \text {$\#$1}^5+10 \text {$\#$1}-5 x^2-10 x-10 c_1\&,1\right ]\\ y(x)&\to \text {Root}\left [2 \text {$\#$1}^5+10 \text {$\#$1}-5 x^2-10 x-10 c_1\&,2\right ]\\ y(x)&\to \text {Root}\left [2 \text {$\#$1}^5+10 \text {$\#$1}-5 x^2-10 x-10 c_1\&,3\right ]\\ y(x)&\to \text {Root}\left [2 \text {$\#$1}^5+10 \text {$\#$1}-5 x^2-10 x-10 c_1\&,4\right ]\\ y(x)&\to \text {Root}\left [2 \text {$\#$1}^5+10 \text {$\#$1}-5 x^2-10 x-10 c_1\&,5\right ] \end{align*}

✓ Sympy. Time used: 0.107 (sec). Leaf size: 17

from sympy import * 
x = symbols("x") 
y = Function("y") 
ode = Eq(-(x + 1)/(y(x)**4 + 1) + Derivative(y(x), x),0) 
ics = {} 
dsolve(ode,func=y(x),ics=ics)
 

\[ - \frac {x^{2}}{2} - x + \frac {y^{5}{\left (x \right )}}{5} + y{\left (x \right )} = C_{1} \]