12.2.32 problem 32

Internal problem ID [1568]
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 : 32
Date solved : Tuesday, March 04, 2025 at 12:39:54 PM
CAS classification : [_linear]

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

With initial conditions

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

✓ Maple. Time used: 0.007 (sec). Leaf size: 14

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

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

✓ Mathematica. Time used: 0.026 (sec). Leaf size: 14

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

\[ y(x)\to -x^2 (\log (x)-1) \]

✓ Sympy. Time used: 0.169 (sec). Leaf size: 10

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

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