70.1.17 problem 17

Internal problem ID [18603]
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 : 17
Date solved : Thursday, October 02, 2025 at 03:15:50 PM
CAS classification : [_separable]

\begin{align*} y^{\prime }&=\frac {3 x}{y+x^{2} y} \end{align*}

With initial conditions

\begin{align*} y \left (0\right )&=-7 \\ \end{align*}

✓ Maple. Time used: 0.089 (sec). Leaf size: 18

ode:=diff(y(x),x) = 3*x/(y(x)+x^2*y(x)); 
ic:=[y(0) = -7]; 
dsolve([ode,op(ic)],y(x), singsol=all);
 

\[ y = -\sqrt {3 \ln \left (x^{2}+1\right )+49} \]

✓ Mathematica. Time used: 0.097 (sec). Leaf size: 21

ode=D[y[x],x]==3*x/(y[x]+x^2*y[x]); 
ic={y[0]==-7}; 
DSolve[{ode,ic},y[x],x,IncludeSingularSolutions->True]
 

\begin{align*} y(x)&\to -\sqrt {3 \log \left (x^2+1\right )+49} \end{align*}

✓ Sympy. Time used: 0.298 (sec). Leaf size: 17

from sympy import * 
x = symbols("x") 
y = Function("y") 
ode = Eq(-3*x/(x**2*y(x) + y(x)) + Derivative(y(x), x),0) 
ics = {y(0): -7} 
dsolve(ode,func=y(x),ics=ics)
 

\[ y{\left (x \right )} = - \sqrt {3 \log {\left (x^{2} + 1 \right )} + 49} \]