12.2.37 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 : Monday, January 27, 2025 at 05:00:47 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*}

✓ Solution by Maple

Time used: 0.007 (sec). Leaf size: 11

dsolve([x*diff(y(x),x)-2*y(x)= -1,y(0) = 1/2],y(x), singsol=all)
 

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

✓ Solution by Mathematica

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

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

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