Internal problem ID [14229]
Book: INTRODUCTORY DIFFERENTIAL EQUATIONS. Martha L. Abell, James P. Braselton.
Fourth edition 2014. ElScAe. 2014
Section: Chapter 2. First Order Equations. Exercises 2.2, page 39
Problem number: 74 (a).
ODE order: 1.
ODE degree: 1.
CAS Maple gives this as type [_separable]
\[ \boxed {y^{\prime }-f \left (t \right ) y=0} \] With initial conditions \begin {align*} [y \left (1\right ) = 1] \end {align*}
✓ Solution by Maple
Time used: 0.063 (sec). Leaf size: 13
dsolve([diff(y(t),t)=f(t)*y(t),y(1) = 1],y(t), singsol=all)
\[ y \left (t \right ) = {\mathrm e}^{\int _{1}^{t}f \left (\textit {\_z1} \right )d \textit {\_z1}} \]
✓ Solution by Mathematica
Time used: 0.028 (sec). Leaf size: 17
DSolve[{y'[t]==f[t]*y[t],{y[1]==1}},y[t],t,IncludeSingularSolutions -> True]
\[ y(t)\to \exp \left (\int _1^tf(K[1])dK[1]\right ) \]