23.4.4 problem 8(d)

Internal problem ID [4169]
Book : Theory and solutions of Ordinary Differential equations, Donald Greenspan, 1960
Section : Chapter 6. Linear systems. Exercises at page 110
Problem number : 8(d)
Date solved : Monday, January 27, 2025 at 08:41:14 AM
CAS classification : system_of_ODEs

\begin{align*} y_{1}^{\prime }\left (x \right )&=4 y_{2} \left (x \right )\\ y_{2}^{\prime }\left (x \right )&=4 y_{2} \left (x \right )-y_{1} \left (x \right ) \end{align*}

✓ Solution by Maple

Time used: 0.019 (sec). Leaf size: 32

dsolve([diff(y__1(x),x)=4*y__2(x),diff(y__2(x),x)=4*y__2(x)-y__1(x)],singsol=all)
 

\begin{align*} y_{1} \left (x \right ) &= {\mathrm e}^{2 x} \left (c_{2} x +c_{1} \right ) \\ y_{2} \left (x \right ) &= \frac {{\mathrm e}^{2 x} \left (2 c_{2} x +2 c_{1} +c_{2} \right )}{4} \\ \end{align*}

✓ Solution by Mathematica

Time used: 0.003 (sec). Leaf size: 46

DSolve[{D[y1[x],x]==4*y2[x],D[y2[x],x]==4*y2[x]-y1[x]},{y1[x],y2[x]},x,IncludeSingularSolutions -> True]
 

\begin{align*} \text {y1}(x)\to e^{2 x} (-2 c_1 x+4 c_2 x+c_1) \\ \text {y2}(x)\to e^{2 x} (c_1 (-x)+2 c_2 x+c_2) \\ \end{align*}