88.12.5 problem 7

Internal problem ID [24061]
Book : Elementary Differential Equations. By Lee Roy Wilcox and Herbert J. Curtis. 1961 first edition. International texbook company. Scranton, Penn. USA. CAT number 61-15976
Section : Chapter 2. Differential equations of first order. Miscellaneous Exercises at page 55
Problem number : 7
Date solved : Thursday, October 02, 2025 at 09:56:34 PM
CAS classification : [[_1st_order, `_with_symmetry_[F(x)*G(y),0]`], [_Abel, `2nd type`, `class C`]]

\begin{align*} y^{\prime }&=\frac {1}{x^{5}+y x} \end{align*}

✓ Maple. Time used: 0.001 (sec). Leaf size: 39

ode:=diff(y(x),x) = 1/(x^5+x*y(x)); 
dsolve(ode,y(x), singsol=all);
 

\[ c_1 +\frac {\operatorname {erf}\left (i y \sqrt {2}\right ) \sqrt {2}\, \sqrt {\pi }\, x^{4}+i {\mathrm e}^{2 y^{2}}}{x^{4}} = 0 \]

✓ Mathematica. Time used: 0.186 (sec). Leaf size: 43

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

\[ \text {Solve}\left [-2 x^4=\frac {2 e^{2 y(x)^2}}{\sqrt {2 \pi } \text {erfi}\left (\sqrt {2} y(x)\right )+2 c_1},y(x)\right ] \]

✓ Sympy. Time used: 0.705 (sec). Leaf size: 37

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

\[ C_{1} - \frac {\sqrt {2} \sqrt {\pi } \operatorname {erfi}{\left (\sqrt {2} y{\left (x \right )} \right )}}{4} - \frac {e^{2 y^{2}{\left (x \right )}}}{4 x^{4}} = 0 \]