88.9.15 problem 15

Internal problem ID [24035]
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. Exercise at page 48
Problem number : 15
Date solved : Thursday, October 02, 2025 at 09:54:58 PM
CAS classification : [_separable]

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

✓ Maple. Time used: 0.007 (sec). Leaf size: 73

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

\begin{align*} y &= \frac {1}{\left ({\mathrm e}^{2 x^{2}} c_1 +1\right )^{{1}/{4}}} \\ y &= -\frac {1}{\left ({\mathrm e}^{2 x^{2}} c_1 +1\right )^{{1}/{4}}} \\ y &= \frac {1}{\sqrt {-\sqrt {{\mathrm e}^{2 x^{2}} c_1 +1}}} \\ y &= -\frac {1}{\sqrt {-\sqrt {{\mathrm e}^{2 x^{2}} c_1 +1}}} \\ \end{align*}

✓ Mathematica. Time used: 1.809 (sec). Leaf size: 128

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

\begin{align*} y(x)&\to -\frac {1}{\sqrt [4]{1+e^{2 x^2+4 c_1}}}\\ y(x)&\to -\frac {i}{\sqrt [4]{1+e^{2 x^2+4 c_1}}}\\ y(x)&\to \frac {i}{\sqrt [4]{1+e^{2 x^2+4 c_1}}}\\ y(x)&\to \frac {1}{\sqrt [4]{1+e^{2 x^2+4 c_1}}}\\ y(x)&\to -1\\ y(x)&\to 0\\ y(x)&\to -i\\ y(x)&\to i\\ y(x)&\to 1 \end{align*}

✓ Sympy. Time used: 2.991 (sec). Leaf size: 78

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

\[ \left [ y{\left (x \right )} = - \sqrt [4]{- \frac {1}{C_{1} e^{2 x^{2}} - 1}}, \ y{\left (x \right )} = - i \sqrt [4]{- \frac {1}{C_{1} e^{2 x^{2}} - 1}}, \ y{\left (x \right )} = i \sqrt [4]{\frac {1}{C_{1} e^{2 x^{2}} + 1}}, \ y{\left (x \right )} = \sqrt [4]{\frac {1}{C_{1} e^{2 x^{2}} + 1}}\right ] \]