Internal problem ID [13046]
Book: DIFFERENTIAL EQUATIONS by Paul Blanchard, Robert L. Devaney, Glen R. Hall. 4th
edition. Brooks/Cole. Boston, USA. 2012
Section: Chapter 1. First-Order Differential Equations. Review Exercises for chapter 1. page
136
Problem number: 31.
ODE order: 1.
ODE degree: 1.
CAS Maple gives this as type [[_linear, `class A`]]
\[ \boxed {y^{\prime }-2 y=\cos \left (4 t \right )} \] With initial conditions \begin {align*} [y \left (0\right ) = 1] \end {align*}
✓ Solution by Maple
Time used: 0.0 (sec). Leaf size: 23
dsolve([diff(y(t),t)= 2*y(t)+cos(4*t),y(0) = 1],y(t), singsol=all)
\[ y \left (t \right ) = -\frac {\cos \left (4 t \right )}{10}+\frac {\sin \left (4 t \right )}{5}+\frac {11 \,{\mathrm e}^{2 t}}{10} \]
✓ Solution by Mathematica
Time used: 0.159 (sec). Leaf size: 29
DSolve[{y'[t]==2*y[t]+Cos[4*t],{y[0]==1}},y[t],t,IncludeSingularSolutions -> True]
\[ y(t)\to \frac {1}{10} \left (11 e^{2 t}+2 \sin (4 t)-\cos (4 t)\right ) \]