Internal problem ID [923]
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.
ODE order: 1.
ODE degree: 1.
CAS Maple gives this as type [_separable]
Solve \begin {gather*} \boxed {y^{\prime } x -2 y+1=0} \end {gather*} With initial conditions \begin {align*} \left [y \relax (0) = {\frac {1}{2}}\right ] \end {align*}
✓ Solution by Maple
Time used: 0.024 (sec). Leaf size: 11
dsolve([x*diff(y(x),x)-2*y(x)= -1,y(0) = 1/2],y(x), singsol=all)
\[ y \relax (x ) = \frac {1}{2}+c_{1} x^{2} \]
✓ Solution by Mathematica
Time used: 0.001 (sec). Leaf size: 8
DSolve[{x*y'[x]-2*y[x]== -1,y[0]==1/2},y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to \frac {1}{2} \\ \end{align*}