Internal problem ID [14458]
Book: INTRODUCTORY DIFFERENTIAL EQUATIONS. Martha L. Abell, James P. Braselton.
Fourth edition 2014. ElScAe. 2014
Section: Chapter 4. Higher Order Equations. Exercises 4.1, page 141
Problem number: 25.
ODE order: 2.
ODE degree: 1.
CAS Maple gives this as type [[_2nd_order, _missing_x]]
\[ \boxed {y^{\prime \prime }-5 y^{\prime }+6 y=0} \] Given that one solution of the ode is \begin {align*} y_1 &= {\mathrm e}^{3 t} \end {align*}
✓ Solution by Maple
Time used: 0.0 (sec). Leaf size: 17
dsolve([diff(y(t),t$2)-5*diff(y(t),t)+6*y(t)=0,exp(3*t)],singsol=all)
\[ y \left (t \right ) = c_{1} {\mathrm e}^{3 t}+c_{2} {\mathrm e}^{2 t} \]
✓ Solution by Mathematica
Time used: 0.012 (sec). Leaf size: 20
DSolve[y''[t]-5*y'[t]+6*y[t]==0,y[t],t,IncludeSingularSolutions -> True]
\[ y(t)\to e^{2 t} \left (c_2 e^t+c_1\right ) \]