7.4.12 problem 12

Internal problem ID [84]
Book : Elementary Differential Equations. By C. Henry Edwards, David E. Penney and David Calvis. 6th edition. 2008
Section : Chapter 1. First order differential equations. Section 1.5 (linear equations). Problems at page 54
Problem number : 12
Date solved : Saturday, March 29, 2025 at 04:30:39 PM
CAS classification : [_linear]

\begin{align*} x y^{\prime }+3 y&=2 x^{5} \end{align*}

With initial conditions

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

✓ Maple. Time used: 0.019 (sec). Leaf size: 14

ode:=x*diff(y(x),x)+3*y(x) = 2*x^5; 
ic:=y(2) = 1; 
dsolve([ode,ic],y(x), singsol=all);
 

\[ y = \frac {x^{8}-224}{4 x^{3}} \]

✓ Mathematica. Time used: 0.029 (sec). Leaf size: 17

ode=x*D[y[x],x]+3*y[x]==2*x^5; 
ic={y[2]==1}; 
DSolve[{ode,ic},y[x],x,IncludeSingularSolutions->True]
 

\[ y(x)\to \frac {x^8-224}{4 x^3} \]

✓ Sympy. Time used: 0.206 (sec). Leaf size: 12

from sympy import * 
x = symbols("x") 
y = Function("y") 
ode = Eq(-2*x**5 + x*Derivative(y(x), x) + 3*y(x),0) 
ics = {y(2): 1} 
dsolve(ode,func=y(x),ics=ics)
 

\[ y{\left (x \right )} = \frac {\frac {x^{8}}{4} - 56}{x^{3}} \]