85.18.2 problem 1 (b)

Internal problem ID [22548]
Book : Applied Differential Equations. By Murray R. Spiegel. 3rd edition. 1980. Pearson. ISBN 978-0130400970
Section : Chapter two. First order and simple higher order ordinary differential equations. A Exercises at page 52
Problem number : 1 (b)
Date solved : Thursday, October 02, 2025 at 08:49:44 PM
CAS classification : [_linear]

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

With initial conditions

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

✓ Maple. Time used: 0.007 (sec). Leaf size: 12

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

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

✓ Mathematica. Time used: 0.02 (sec). Leaf size: 13

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

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

✓ Sympy. Time used: 0.146 (sec). Leaf size: 8

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

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