6.2.31 problem 31

Internal problem ID [1567]
Book : Elementary differential equations with boundary value problems. William F. Trench. Brooks/Cole 2001
Section : Chapter 2, First order equations. Linear first order. Section 2.1 Page 41
Problem number : 31
Date solved : Tuesday, September 30, 2025 at 04:36:39 AM
CAS classification : [_linear]

\begin{align*} x y^{\prime }+2 y&=8 x^{2} \end{align*}

With initial conditions

\begin{align*} y \left (1\right )&=3 \\ \end{align*}

✓ Maple. Time used: 0.006 (sec). Leaf size: 15

ode:=x*diff(y(x),x)+2*y(x) = 8*x^2; 
ic:=[y(1) = 3]; 
dsolve([ode,op(ic)],y(x), singsol=all);
 

\[ y = \frac {2 x^{4}+1}{x^{2}} \]

✓ Mathematica. Time used: 0.017 (sec). Leaf size: 14

ode=x*D[y[x],x]+2*y[x]==8*x^2; 
ic=y[1]==3; 
DSolve[{ode,ic},y[x],x,IncludeSingularSolutions->True]
 

\begin{align*} y(x)&\to 2 x^2+\frac {1}{x^2} \end{align*}

✓ Sympy. Time used: 0.105 (sec). Leaf size: 12

from sympy import * 
x = symbols("x") 
y = Function("y") 
ode = Eq(-8*x**2 + x*Derivative(y(x), x) + 2*y(x),0) 
ics = {y(1): 3} 
dsolve(ode,func=y(x),ics=ics)
 

\[ y{\left (x \right )} = \frac {2 x^{4} + 1}{x^{2}} \]