6.2.37 problem 44

Internal problem ID [1573]
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 : 44
Date solved : Tuesday, September 30, 2025 at 04:36:57 AM
CAS classification : [_separable]

\begin{align*} x y^{\prime }-2 y&=-1 \end{align*}

With initial conditions

\begin{align*} y \left (0\right )&={\frac {1}{2}} \\ \end{align*}

✓ Maple. Time used: 0.041 (sec). Leaf size: 11

ode:=x*diff(y(x),x)-2*y(x) = -1; 
ic:=[y(0) = 1/2]; 
dsolve([ode,op(ic)],y(x), singsol=all);
 

\[ y = \frac {1}{2}+c_1 \,x^{2} \]

✓ Mathematica. Time used: 0.001 (sec). Leaf size: 8

ode=x*D[y[x],x]-2*y[x]== -1; 
ic=y[0]==1/2; 
DSolve[{ode,ic},y[x],x,IncludeSingularSolutions->True]
 

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

✗ Sympy

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

ValueError : Couldnt solve for initial conditions