71.18.7 problem 6 a

Internal problem ID [14581]
Book : Ordinary Differential Equations by Charles E. Roberts, Jr. CRC Press. 2010
Section : Chapter 8. Linear Systems of First-Order Differential Equations. Exercises 8.3 page 379
Problem number : 6 a
Date solved : Tuesday, January 28, 2025 at 08:25:31 PM
CAS classification : system_of_ODEs

\begin{align*} y_{1}^{\prime }\left (x \right )&=\frac {5 y_{1} \left (x \right )}{x}+\frac {4 y_{2} \left (x \right )}{x}\\ y_{2}^{\prime }\left (x \right )&=-\frac {6 y_{1} \left (x \right )}{x}-\frac {5 y_{2} \left (x \right )}{x} \end{align*}

✓ Solution by Maple

Time used: 0.053 (sec). Leaf size: 33

dsolve([diff(y__1(x),x)=5/x*y__1(x)+4/x*y__2(x),diff(y__2(x),x)=-6/x*y__1(x)-5/x*y__2(x)],singsol=all)
 

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

✓ Solution by Mathematica

Time used: 0.008 (sec). Leaf size: 34

DSolve[{D[ y1[x],x]==5/x*y1[x]+4/x*y2[x],D[ y2[x],x]==-6/x*y1[x]-5/x*y2[x]},{y1[x],y2[x]},x,IncludeSingularSolutions -> True]
 

\begin{align*} \text {y1}(x)\to \frac {c_1}{x}+c_2 x \\ \text {y2}(x)\to -\frac {3 c_1}{2 x}-c_2 x \\ \end{align*}