36.1.2 problem 2

Internal problem ID [6257]
Book : Fundamentals of Differential Equations. By Nagle, Saff and Snider. 9th edition. Boston. Pearson 2018.
Section : Chapter 2, First order differential equations. Section 2.2, Separable Equations. Exercises. page 46
Problem number : 2
Date solved : Sunday, March 30, 2025 at 10:44:54 AM
CAS classification : [_quadrature]

\begin{align*} y^{\prime }&=4 y^{2}-3 y+1 \end{align*}

✓ Maple. Time used: 0.005 (sec). Leaf size: 20

ode:=diff(y(x),x) = 4*y(x)^2-3*y(x)+1; 
dsolve(ode,y(x), singsol=all);
 

\[ y = \frac {3}{8}+\frac {\sqrt {7}\, \tan \left (\frac {\left (c_1 +x \right ) \sqrt {7}}{2}\right )}{8} \]

✓ Mathematica. Time used: 1.745 (sec). Leaf size: 69

ode=D[y[x],x]==4*y[x]^2-3*y[x]+1; 
ic={}; 
DSolve[{ode,ic},y[x],x,IncludeSingularSolutions->True]
 

\begin{align*} y(x)\to \frac {1}{8} \left (3+\sqrt {7} \tan \left (\frac {1}{2} \sqrt {7} (x+c_1)\right )\right ) \\ y(x)\to \frac {1}{8} \left (3-i \sqrt {7}\right ) \\ y(x)\to \frac {1}{8} \left (3+i \sqrt {7}\right ) \\ \end{align*}

✓ Sympy. Time used: 0.381 (sec). Leaf size: 24

from sympy import * 
x = symbols("x") 
y = Function("y") 
ode = Eq(-4*y(x)**2 + 3*y(x) + Derivative(y(x), x) - 1,0) 
ics = {} 
dsolve(ode,func=y(x),ics=ics)
 

\[ y{\left (x \right )} = - \frac {\sqrt {7} \tan {\left (C_{1} - \frac {\sqrt {7} x}{2} \right )}}{8} + \frac {3}{8} \]