6.2.35 problem 35

Internal problem ID [1571]
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 : 35
Date solved : Tuesday, September 30, 2025 at 04:36:53 AM
CAS classification : [_linear]

\begin{align*} \left (x +2\right ) y^{\prime }+4 y&=\frac {2 x^{2}+1}{x \left (x +2\right )^{3}} \end{align*}

With initial conditions

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

✓ Maple. Time used: 0.035 (sec). Leaf size: 20

ode:=(x+2)*diff(y(x),x)+4*y(x) = (2*x^2+1)/x/(x+2)^3; 
ic:=[y(-1) = 2]; 
dsolve([ode,op(ic)],y(x), singsol=all);
 

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

✓ Mathematica. Time used: 0.031 (sec). Leaf size: 23

ode=(x+2)*D[y[x],x]+4*y[x]== (1+2*x^2)/(x*(x+2)^3); 
ic=y[-1]==2; 
DSolve[{ode,ic},y[x],x,IncludeSingularSolutions->True]
 

\begin{align*} y(x)&\to \frac {x^2+\log (x)-i \pi +1}{(x+2)^4} \end{align*}

✓ Sympy. Time used: 0.280 (sec). Leaf size: 32

from sympy import * 
x = symbols("x") 
y = Function("y") 
ode = Eq((x + 2)*Derivative(y(x), x) + 4*y(x) - (2*x**2 + 1)/(x*(x + 2)**3),0) 
ics = {y(-1): 2} 
dsolve(ode,func=y(x),ics=ics)
 

\[ y{\left (x \right )} = \frac {x^{2} + \log {\left (x \right )} + 1 - i \pi }{x^{4} + 8 x^{3} + 24 x^{2} + 32 x + 16} \]