76.1.17 problem 17

Internal problem ID [17245]
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 : Monday, March 31, 2025 at 03:46:05 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,ic],y(x), singsol=all);
 

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

✓ Mathematica. Time used: 0.111 (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]
 

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

✓ Sympy. Time used: 0.460 (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)
 

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