Internal problem ID [14492]
Book: INTRODUCTORY DIFFERENTIAL EQUATIONS. Martha L. Abell, James P. Braselton.
Fourth edition 2014. ElScAe. 2014
Section: Chapter 4. Higher Order Equations. Exercises 4.2, page 147
Problem number: 19.
ODE order: 2.
ODE degree: 1.
CAS Maple gives this as type [[_2nd_order, _missing_x]]
\[ \boxed {y^{\prime \prime }-7 y^{\prime }+12 y=0} \] With initial conditions \begin {align*} [y \left (0\right ) = 3, y^{\prime }\left (0\right ) = -2] \end {align*}
✓ Solution by Maple
Time used: 0.0 (sec). Leaf size: 17
dsolve([diff(y(t),t$2)-7*diff(y(t),t)+12*y(t)=0,y(0) = 3, D(y)(0) = -2],y(t), singsol=all)
\[ y \left (t \right ) = -11 \,{\mathrm e}^{4 t}+14 \,{\mathrm e}^{3 t} \]
✓ Solution by Mathematica
Time used: 0.022 (sec). Leaf size: 18
DSolve[{y''[t]-7*y'[t]+12*y[t]==0,{y[0]==3,y'[0]==-2}},y[t],t,IncludeSingularSolutions -> True]
\[ y(t)\to e^{3 t} \left (14-11 e^t\right ) \]