88.9.12 problem 12

Internal problem ID [24032]
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 : 12
Date solved : Thursday, October 02, 2025 at 09:54:46 PM
CAS classification : [_Bernoulli]

\begin{align*} y^{\prime }-4 y&=x y^{3} \end{align*}

✓ Maple. Time used: 0.003 (sec). Leaf size: 39

ode:=diff(y(x),x)-4*y(x) = x*y(x)^3; 
dsolve(ode,y(x), singsol=all);
 

\begin{align*} y &= -\frac {8}{\sqrt {2+64 \,{\mathrm e}^{-8 x} c_1 -16 x}} \\ y &= \frac {8}{\sqrt {2+64 \,{\mathrm e}^{-8 x} c_1 -16 x}} \\ \end{align*}

✓ Mathematica. Time used: 1.752 (sec). Leaf size: 76

ode=D[y[x],{x,1}]-4*y[x]==x*y[x]^3; 
ic={}; 
DSolve[{ode,ic},y[x],x,IncludeSingularSolutions->True]
 

\begin{align*} y(x)&\to -\frac {4 i e^{4 x}}{\sqrt {e^{8 x} \left (4 x-\frac {1}{2}\right )-16 c_1}}\\ y(x)&\to \frac {4 i e^{4 x}}{\sqrt {e^{8 x} \left (4 x-\frac {1}{2}\right )-16 c_1}}\\ y(x)&\to 0 \end{align*}

✓ Sympy. Time used: 0.846 (sec). Leaf size: 66

from sympy import * 
x = symbols("x") 
y = Function("y") 
ode = Eq(-x*y(x)**3 - 4*y(x) + Derivative(y(x), x),0) 
ics = {} 
dsolve(ode,func=y(x),ics=ics)
 

\[ \left [ y{\left (x \right )} = - 4 \sqrt {2} \sqrt {\frac {e^{8 x}}{C_{1} - 8 x e^{8 x} + e^{8 x}}}, \ y{\left (x \right )} = 4 \sqrt {2} \sqrt {\frac {e^{8 x}}{C_{1} - 8 x e^{8 x} + e^{8 x}}}\right ] \]