67.6.6 problem Problem 4(f)

Internal problem ID [14110]
Book : APPLIED DIFFERENTIAL EQUATIONS The Primary Course by Vladimir A. Dobrushkin. CRC Press 2015
Section : Chapter 6.4 Reduction to a single ODE. Problems page 415
Problem number : Problem 4(f)
Date solved : Tuesday, January 28, 2025 at 06:14:35 AM
CAS classification : system_of_ODEs

\begin{align*} x^{\prime }\left (t \right )-4 y^{\prime }&=0\\ 2 x^{\prime }\left (t \right )-3 y^{\prime }&=y+t \end{align*}

✓ Solution by Maple

Time used: 0.055 (sec). Leaf size: 31

dsolve([diff(x(t),t)-4*diff(y(t),t)=0,2*diff(x(t),t)-3*diff(y(t),t)=y(t)+t],singsol=all)
 

\begin{align*} x \left (t \right ) &= 5 \,{\mathrm e}^{\frac {t}{5}} c_{1} -4 t +c_{2} \\ y &= \frac {5 \,{\mathrm e}^{\frac {t}{5}} c_{1}}{4}-5-t \\ \end{align*}

✓ Solution by Mathematica

Time used: 0.023 (sec). Leaf size: 109

DSolve[{D[x[t],t]-4*D[y[t],t]==0,2*D[x[t],t]-3*D[y[t],t]==y[t]+t},{x[t],y[t]},t,IncludeSingularSolutions -> True]
 

\begin{align*} x(t)\to \int _1^t\frac {4}{5} e^{-\frac {K[1]}{5}} K[1]dK[1]+4 \left (e^{t/5}-1\right ) \int _1^t\frac {1}{5} e^{-\frac {K[2]}{5}} K[2]dK[2]+4 c_2 \left (e^{t/5}-1\right )+c_1 \\ y(t)\to e^{t/5} \left (\int _1^t\frac {1}{5} e^{-\frac {K[2]}{5}} K[2]dK[2]+c_2\right ) \\ \end{align*}