12.1.13 problem 5(b)

Internal problem ID [1531]
Book : Elementary differential equations with boundary value problems. William F. Trench. Brooks/Cole 2001
Section : Chapter 1, Introduction. Section 1.2 Page 14
Problem number : 5(b)
Date solved : Saturday, March 29, 2025 at 10:57:49 PM
CAS classification : [_linear]

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

With initial conditions

\begin{align*} y \left (1\right )&={\frac {3}{2}} \end{align*}

✓ Maple. Time used: 0.029 (sec). Leaf size: 19

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

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

✓ Mathematica. Time used: 0.031 (sec). Leaf size: 19

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

\[ y(x)\to \frac {1}{x^2}+\frac {2 \log (x)}{x^2}+\frac {1}{2} \]

✓ Sympy. Time used: 0.230 (sec). Leaf size: 17

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

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