81.8.1 problem 8

Internal problem ID [18711]
Book : A short course on differential equations. By Donald Francis Campbell. Maxmillan company. London. 1907
Section : Chapter VII. Ordinary differential equations in two dependent variables. Exercises at page 86
Problem number : 8
Date solved : Tuesday, January 28, 2025 at 12:12:11 PM
CAS classification : system_of_ODEs

\begin{align*} \frac {d}{d x}z \left (x \right )+7 y \left (x \right )-3 z \left (x \right )&=0\\ 7 \frac {d}{d x}y \left (x \right )+63 y \left (x \right )-36 z \left (x \right )&=0 \end{align*}

✓ Solution by Maple

Time used: 0.017 (sec). Leaf size: 32

dsolve([diff(z(x),x)+7*y(x)-3*z(x)=0,7*diff(y(x),x)+63*y(x)-36*z(x)=0],singsol=all)
 

\begin{align*} y \left (x \right ) &= {\mathrm e}^{-3 x} \left (c_{2} x +c_{1} \right ) \\ z \left (x \right ) &= \frac {7 \,{\mathrm e}^{-3 x} \left (6 c_{2} x +6 c_{1} +c_{2} \right )}{36} \\ \end{align*}

✓ Solution by Mathematica

Time used: 0.003 (sec). Leaf size: 50

DSolve[{D[z[x],x]+7*y[x]-3*z[x]==0,7*D[y[x],x]+63*y[x]-36*z[x]==0},{y[x],z[x]},x,IncludeSingularSolutions -> True]
 

\begin{align*} y(x)\to \frac {1}{7} e^{-3 x} (c_1 (7-42 x)+36 c_2 x) \\ z(x)\to e^{-3 x} (-7 c_1 x+6 c_2 x+c_2) \\ \end{align*}