76.1.13 problem 13

Internal problem ID [17241]
Book : Differential equations. An introduction to modern methods and applications. James Brannan, William E. Boyce. Third edition. Wiley 2015
Section : Chapter 2. First order differential equations. Section 2.1 (Separable equations). Problems at page 44
Problem number : 13
Date solved : Monday, March 31, 2025 at 03:45:52 PM
CAS classification : [_separable]

\begin{align*} y^{\prime }&=\left (1-12 x \right ) y^{2} \end{align*}

With initial conditions

\begin{align*} y \left (0\right )&=-{\frac {1}{8}} \end{align*}

✓ Maple. Time used: 0.110 (sec). Leaf size: 16

ode:=diff(y(x),x) = (1-12*x)*y(x)^2; 
ic:=y(0) = -1/8; 
dsolve([ode,ic],y(x), singsol=all);
 

\[ y = \frac {1}{6 x^{2}-x -8} \]

✓ Mathematica. Time used: 0.145 (sec). Leaf size: 17

ode=D[y[x],x]==(1-12*x)*y[x]^2; 
ic={y[0]==-1/8}; 
DSolve[{ode,ic},y[x],x,IncludeSingularSolutions->True]
 

\[ y(x)\to \frac {1}{6 x^2-x-8} \]

✓ Sympy. Time used: 0.179 (sec). Leaf size: 12

from sympy import * 
x = symbols("x") 
y = Function("y") 
ode = Eq(-(1 - 12*x)*y(x)**2 + Derivative(y(x), x),0) 
ics = {y(0): -1/8} 
dsolve(ode,func=y(x),ics=ics)
 

\[ y{\left (x \right )} = \frac {1}{6 x^{2} - x - 8} \]