23.4.8 problem 9

Internal problem ID [4173]
Book : Theory and solutions of Ordinary Differential equations, Donald Greenspan, 1960
Section : Chapter 6. Linear systems. Exercises at page 110
Problem number : 9
Date solved : Monday, January 27, 2025 at 08:41:17 AM
CAS classification : system_of_ODEs

\begin{align*} 2 y_{1}^{\prime }\left (x \right )&=y_{1} \left (x \right )+y_{2} \left (x \right )\\ 2 y_{2}^{\prime }\left (x \right )&=5 y_{2} \left (x \right )-3 y_{1} \left (x \right ) \end{align*}

With initial conditions

\begin{align*} y_{1} \left (0\right ) = 3\\ y_{2} \left (0\right ) = 7 \end{align*}

✓ Solution by Maple

Time used: 0.031 (sec). Leaf size: 25

dsolve([2*diff(y__1(x),x) = y__1(x)+y__2(x), 2*diff(y__2(x),x) = 5*y__2(x)-3*y__1(x), y__1(0) = 3, y__2(0) = 7], singsol=all)
 

\begin{align*} y_{1} \left (x \right ) &= {\mathrm e}^{x}+2 \,{\mathrm e}^{2 x} \\ y_{2} \left (x \right ) &= {\mathrm e}^{x}+6 \,{\mathrm e}^{2 x} \\ \end{align*}

✓ Solution by Mathematica

Time used: 0.004 (sec). Leaf size: 30

DSolve[{2*D[y1[x],x]==y1[x]+y2[x],2*D[y2[x],x]==5*y2[x]-3*y1[x]},{y1[0]==3,y2[0]==7},{y1[x],y2[x]},x,IncludeSingularSolutions -> True]
 

\begin{align*} \text {y1}(x)\to e^x \left (2 e^x+1\right ) \\ \text {y2}(x)\to e^x \left (6 e^x+1\right ) \\ \end{align*}