7.7.7 problem 7

Internal problem ID [185]
Book : Elementary Differential Equations. By C. Henry Edwards, David E. Penney and David Calvis. 6th edition. 2008
Section : Chapter 1. First order differential equations. Review problems at page 98
Problem number : 7
Date solved : Saturday, March 29, 2025 at 04:38:45 PM
CAS classification : [_linear]

\begin{align*} 2 x^{2} y+x^{3} y^{\prime }&=1 \end{align*}

✓ Maple. Time used: 0.001 (sec). Leaf size: 12

ode:=2*x^2*y(x)+x^3*diff(y(x),x) = 1; 
dsolve(ode,y(x), singsol=all);
 

\[ y = \frac {\ln \left (x \right )+c_1}{x^{2}} \]

✓ Mathematica. Time used: 0.029 (sec). Leaf size: 14

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

\[ y(x)\to \frac {\log (x)+c_1}{x^2} \]

✓ Sympy. Time used: 0.349 (sec). Leaf size: 10

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

\[ y{\left (x \right )} = \frac {C_{1} + \log {\left (x \right )}}{x^{2}} \]