29.8.25 problem 25

Internal problem ID [7367]
Book : Mathematical Methods in the Physical Sciences. third edition. Mary L. Boas. John Wiley. 2006
Section : Chapter 8, Ordinary differential equations. Section 13. Miscellaneous problems. page 466
Problem number : 25
Date solved : Tuesday, September 30, 2025 at 04:29:53 PM
CAS classification : [_separable]

\begin{align*} 3 x^{2} y+x^{3} y^{\prime }&=0 \end{align*}

With initial conditions

\begin{align*} y \left (1\right )&=2 \\ \end{align*}

✓ Maple. Time used: 0.005 (sec). Leaf size: 9

ode:=3*x^2*y(x)+x^3*diff(y(x),x) = 0; 
ic:=[y(1) = 2]; 
dsolve([ode,op(ic)],y(x), singsol=all);
 

\[ y = \frac {2}{x^{3}} \]

✓ Mathematica. Time used: 0.022 (sec). Leaf size: 10

ode=3*x^2*y[x]+x^3*D[y[x],x]==0; 
ic={y[1]==2}; 
DSolve[{ode,ic},y[x],x,IncludeSingularSolutions->True]
 

\begin{align*} y(x)&\to \frac {2}{x^3} \end{align*}

✓ Sympy. Time used: 0.068 (sec). Leaf size: 7

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

\[ y{\left (x \right )} = \frac {2}{x^{3}} \]