2.4.12 problem 12

Internal problem ID [715]
Book : Differential equations and linear algebra, 3rd ed., Edwards and Penney
Section : Section 1.5. Linear first order equations. Page 56
Problem number : 12
Date solved : Tuesday, September 30, 2025 at 04:06:55 AM
CAS classification : [_linear]

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

With initial conditions

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

✓ Maple. Time used: 0.005 (sec). Leaf size: 14

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

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

✓ Mathematica. Time used: 0.016 (sec). Leaf size: 17

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

\begin{align*} y(x)&\to \frac {x^8-224}{4 x^3} \end{align*}

✓ Sympy. Time used: 0.118 (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)
 

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