Internal problem ID [896]
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: 10.
ODE order: 1.
ODE degree: 1.
CAS Maple gives this as type [_separable]
Solve \begin {gather*} \boxed {y^{\prime }+\frac {k y}{x}=0} \end {gather*} With initial conditions \begin {align*} [y \relax (1) = 3] \end {align*}
✓ Solution by Maple
Time used: 0.009 (sec). Leaf size: 11
dsolve([diff(y(x),x) +k/x*y(x)=0,y(1) = 3],y(x), singsol=all)
\[ y \relax (x ) = 3 x^{-k} \]
✓ Solution by Mathematica
Time used: 0.025 (sec). Leaf size: 12
DSolve[{y'[x] +k/x*y[x]==0,y[1]==3},y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to 3 x^{-k} \\ \end{align*}