67.7.4 problem Problem 3(d)

Internal problem ID [14115]
Book : APPLIED DIFFERENTIAL EQUATIONS The Primary Course by Vladimir A. Dobrushkin. CRC Press 2015
Section : Chapter 8.3 Systems of Linear Differential Equations (Variation of Parameters). Problems page 514
Problem number : Problem 3(d)
Date solved : Tuesday, January 28, 2025 at 06:14:40 AM
CAS classification : system_of_ODEs

\begin{align*} x^{\prime }\left (t \right )&=-14 x \left (t \right )+39 y+78 \sinh \left (t \right )\\ y^{\prime }&=-6 x \left (t \right )+16 y+6 \cosh \left (t \right ) \end{align*}

✓ Solution by Maple

Time used: 1.367 (sec). Leaf size: 85

dsolve([diff(x(t),t)=-14*x(t)+39*y(t)+78*sinh(t),diff(y(t),t)=-6*x(t)+16*y(t)+6*cosh(t)],singsol=all)
 

\begin{align*} x \left (t \right ) &= {\mathrm e}^{t} \sin \left (3 t \right ) c_{2} +{\mathrm e}^{t} \cos \left (3 t \right ) c_{1} +60 \,{\mathrm e}^{-t}-52 \,{\mathrm e}^{t} \\ y &= \frac {5 \,{\mathrm e}^{t} \sin \left (3 t \right ) c_{2}}{13}+\frac {{\mathrm e}^{t} \cos \left (3 t \right ) c_{2}}{13}+\frac {5 \,{\mathrm e}^{t} \cos \left (3 t \right ) c_{1}}{13}-\frac {{\mathrm e}^{t} \sin \left (3 t \right ) c_{1}}{13}+20 \,{\mathrm e}^{-t}-20 \,{\mathrm e}^{t}-2 \sinh \left (t \right ) \\ \end{align*}

✓ Solution by Mathematica

Time used: 15.400 (sec). Leaf size: 1975

DSolve[{D[x[t],t]==-14*x[t]+39*y[t]+78*Sinh[t],D[y[t],t]==-6*x[t]+16*y[t]+6*Cosh[t]},{x[t],y[t]},t,IncludeSingularSolutions -> True]
 

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