28.4.7 problem 7.7

Internal problem ID [4539]
Book : Differential equations for engineers by Wei-Chau XIE, Cambridge Press 2010
Section : Chapter 7. Systems of linear differential equations. Problems at page 351
Problem number : 7.7
Date solved : Monday, January 27, 2025 at 09:23:13 AM
CAS classification : system_of_ODEs

\begin{align*} \frac {d}{d x}y_{1} \left (x \right )-2 y_{1} \left (x \right )+3 y_{2} \left (x \right )-3 y_{3} \left (x \right )&=0\\ -4 y_{1} \left (x \right )+\frac {d}{d x}y_{2} \left (x \right )+5 y_{2} \left (x \right )-3 y_{3} \left (x \right )&=0\\ -4 y_{1} \left (x \right )+4 y_{2} \left (x \right )+\frac {d}{d x}y_{3} \left (x \right )-2 y_{3} \left (x \right )&=0 \end{align*}

✓ Solution by Maple

Time used: 0.053 (sec). Leaf size: 55

dsolve([diff(y__1(x),x)-2*y__1(x)+3*y__2(x)-3*y__3(x)=0, -4*y__1(x)+diff(y__2(x),x)+5*y__2(x)-3*y__3(x)=0, -4*y__1(x)+4*y__2(x)+diff(y__3(x),x)-2*y__3(x)=0],singsol=all)
 

\begin{align*} y_{1} \left (x \right ) &= c_{2} {\mathrm e}^{-x}+c_3 \,{\mathrm e}^{2 x} \\ y_{2} \left (x \right ) &= c_{2} {\mathrm e}^{-x}+c_3 \,{\mathrm e}^{2 x}+{\mathrm e}^{-2 x} c_{1} \\ y_{3} \left (x \right ) &= c_3 \,{\mathrm e}^{2 x}+{\mathrm e}^{-2 x} c_{1} \\ \end{align*}

✓ Solution by Mathematica

Time used: 0.004 (sec). Leaf size: 91

DSolve[{D[y1[x],x]-2*y1[x]+3*y2[x]-3*y2[x]==0,-4*y1[x]+D[y2[x],x]+5*y2[x]-3*y3[x]==0, -4*y1[x]+4*y2[x]+D[y3[x],x]-2*y3[x]==0},{y1[x],y2[x],y3[x]},x,IncludeSingularSolutions -> True]
 

\begin{align*} \text {y1}(x)\to c_1 e^{2 x} \\ \text {y2}(x)\to e^{-2 x} \left (c_1 \left (e^{4 x}-1\right )+c_2 \left (4-3 e^x\right )+3 c_3 \left (e^x-1\right )\right ) \\ \text {y3}(x)\to e^{-2 x} \left (c_1 \left (e^{4 x}-1\right )-4 c_2 \left (e^x-1\right )+c_3 \left (4 e^x-3\right )\right ) \\ \end{align*}