8.4.14 problem 14

Internal problem ID [717]
Book : Differential equations and linear algebra, 3rd ed., Edwards and Penney
Section : Section 1.5. Linear first order equations. Page 56
Problem number : 14
Date solved : Tuesday, March 04, 2025 at 11:33:57 AM
CAS classification : [_linear]

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

With initial conditions

\begin{align*} y \left (1\right )&=10 \end{align*}

✓ Maple. Time used: 0.006 (sec). Leaf size: 12

ode:=-3*y(x)+x*diff(y(x),x) = x^3; 
ic:=y(1) = 10; 
dsolve([ode,ic],y(x), singsol=all);
 

\[ y = \left (\ln \left (x \right )+10\right ) x^{3} \]

✓ Mathematica. Time used: 0.026 (sec). Leaf size: 13

ode=-3*y[x]+x*D[y[x],x] == x^3; 
ic=y[1]==10; 
DSolve[{ode,ic},y[x],x,IncludeSingularSolutions->True]
 

\[ y(x)\to x^3 (\log (x)+10) \]

✓ Sympy. Time used: 0.268 (sec). Leaf size: 10

from sympy import * 
x = symbols("x") 
y = Function("y") 
ode = Eq(-x**3 + x*Derivative(y(x), x) - 3*y(x),0) 
ics = {y(1): 10} 
dsolve(ode,func=y(x),ics=ics)
 

\[ y{\left (x \right )} = x^{3} \left (\log {\left (x \right )} + 10\right ) \]