Internal problem ID [14462]
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: 29.
ODE order: 2.
ODE degree: 1.
CAS Maple gives this as type [[_2nd_order, _missing_x]]
\[ \boxed {y^{\prime \prime }+9 y=0} \] Given that one solution of the ode is \begin {align*} y_1 &= \cos \left (3 t \right ) \end {align*}
With initial conditions \begin {align*} [y \left (0\right ) = 1, y^{\prime }\left (0\right ) = -4] \end {align*}
✓ Solution by Maple
Time used: 0.016 (sec). Leaf size: 15
dsolve([diff(diff(y(t),t),t)+9*y(t) = 0, cos(3*t), y(0) = 1, D(y)(0) = -4], singsol=all)
\[ y \left (t \right ) = \cos \left (3 t \right )-\frac {4 \sin \left (3 t \right )}{3} \]
✓ Solution by Mathematica
Time used: 0.012 (sec). Leaf size: 18
DSolve[y''[t]+9*y[t]==0,{y[0]==1,y'[0]==-4},y[t],t,IncludeSingularSolutions -> True]
\[ y(t)\to \cos (3 t)-\frac {4}{3} \sin (3 t) \]