Internal problem ID [13167]
Book: DIFFERENTIAL EQUATIONS by Paul Blanchard, Robert L. Devaney, Glen R. Hall. 4th
edition. Brooks/Cole. Boston, USA. 2012
Section: Chapter 4. Forcing and Resonance. Section 4.1 page 399
Problem number: 7.
ODE order: 2.
ODE degree: 1.
CAS Maple gives this as type [[_2nd_order, _with_linear_symmetries]]
\[ \boxed {y^{\prime \prime }-5 y^{\prime }+4 y={\mathrm e}^{4 t}} \]
✓ Solution by Maple
Time used: 0.0 (sec). Leaf size: 20
dsolve(diff(y(t),t$2)-5*diff(y(t),t)+4*y(t)=exp(4*t),y(t), singsol=all)
\[ y \left (t \right ) = \frac {\left (t +3 c_{2} \right ) {\mathrm e}^{4 t}}{3}+c_{1} {\mathrm e}^{t} \]
✓ Solution by Mathematica
Time used: 0.038 (sec). Leaf size: 29
DSolve[y''[t]-5*y'[t]+4*y[t]==Exp[4*t],y[t],t,IncludeSingularSolutions -> True]
\[ y(t)\to c_1 e^t+e^{4 t} \left (\frac {t}{3}-\frac {1}{9}+c_2\right ) \]