23.4.1 problem 8(a)

Internal problem ID [4166]
Book : Theory and solutions of Ordinary Differential equations, Donald Greenspan, 1960
Section : Chapter 6. Linear systems. Exercises at page 110
Problem number : 8(a)
Date solved : Monday, January 27, 2025 at 08:41:11 AM
CAS classification : system_of_ODEs

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

✓ Solution by Maple

Time used: 0.029 (sec). Leaf size: 30

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

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

✓ Solution by Mathematica

Time used: 0.003 (sec). Leaf size: 54

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

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