76.1.4 problem 4

Internal problem ID [17232]
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 : 4
Date solved : Monday, March 31, 2025 at 03:45:18 PM
CAS classification : [_separable]

\begin{align*} y^{\prime }&=\frac {7 x^{2}-1}{7+5 y} \end{align*}

✓ Maple. Time used: 0.003 (sec). Leaf size: 45

ode:=diff(y(x),x) = (7*x^2-1)/(7+5*y(x)); 
dsolve(ode,y(x), singsol=all);
 

\begin{align*} y &= -\frac {7}{5}-\frac {\sqrt {210 x^{3}+90 c_1 -90 x +441}}{15} \\ y &= -\frac {7}{5}+\frac {\sqrt {210 x^{3}+90 c_1 -90 x +441}}{15} \\ \end{align*}

✓ Mathematica. Time used: 0.154 (sec). Leaf size: 59

ode=D[y[x],x]==(7*x^2-1)/(7+5*y[x]); 
ic={}; 
DSolve[{ode,ic},y[x],x,IncludeSingularSolutions->True]
 

\begin{align*} y(x)\to \frac {1}{15} \left (-21-\sqrt {210 x^3-90 x+441+90 c_1}\right ) \\ y(x)\to \frac {1}{15} \left (-21+\sqrt {210 x^3-90 x+441+90 c_1}\right ) \\ \end{align*}

✓ Sympy. Time used: 0.444 (sec). Leaf size: 42

from sympy import * 
x = symbols("x") 
y = Function("y") 
ode = Eq(-(7*x**2 - 1)/(5*y(x) + 7) + Derivative(y(x), x),0) 
ics = {} 
dsolve(ode,func=y(x),ics=ics)
 

\[ \left [ y{\left (x \right )} = - \frac {\sqrt {C_{1} + 210 x^{3} - 90 x}}{15} - \frac {7}{5}, \ y{\left (x \right )} = \frac {\sqrt {C_{1} + 210 x^{3} - 90 x}}{15} - \frac {7}{5}\right ] \]