Internal problem ID [14460]
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: 27.
ODE order: 2.
ODE degree: 1.
CAS Maple gives this as type [[_2nd_order, _missing_x]]
\[ \boxed {y^{\prime \prime }-4 y^{\prime }+4 y=0} \] Given that one solution of the ode is \begin {align*} y_1 &= {\mathrm e}^{2 t} \end {align*}
With initial conditions \begin {align*} [y \left (0\right ) = 0, y^{\prime }\left (0\right ) = 1] \end {align*}
✓ Solution by Maple
Time used: 0.0 (sec). Leaf size: 10
dsolve([diff(diff(y(t),t),t)-4*diff(y(t),t)+4*y(t) = 0, exp(2*t), y(0) = 0, D(y)(0) = 1], singsol=all)
\[ y \left (t \right ) = {\mathrm e}^{2 t} t \]
✓ Solution by Mathematica
Time used: 0.014 (sec). Leaf size: 12
DSolve[y''[t]-4*y'[t]+4*y[t]==0,{y[0]==0,y'[0]==1},y[t],t,IncludeSingularSolutions -> True]
\[ y(t)\to e^{2 t} t \]