77.1.164 problem 191 (page 298)

Internal problem ID [18054]
Book : V.V. Stepanov, A course of differential equations (in Russian), GIFML. Moscow (1958)
Section : All content
Problem number : 191 (page 298)
Date solved : Tuesday, January 28, 2025 at 08:28:32 PM
CAS classification : system_of_ODEs

\begin{align*} \left (\frac {d}{d t}x \left (t \right )\right ) t +6 x \left (t \right )-y \left (t \right )-3 z \left (t \right )&=0\\ \left (\frac {d}{d t}y \left (t \right )\right ) t +23 x \left (t \right )-6 y \left (t \right )-9 z \left (t \right )&=0\\ \left (\frac {d}{d t}z \left (t \right )\right ) t +x \left (t \right )+y \left (t \right )-2 z \left (t \right )&=0 \end{align*}

✓ Solution by Maple

Time used: 0.132 (sec). Leaf size: 63

dsolve([t*diff(x(t),t)+6*x(t)-y(t)-3*z(t)=0,t*diff(y(t),t)+23*x(t)-6*y(t)-9*z(t)=0,t*diff(z(t),t)+x(t)+y(t)-2*z(t)=0],singsol=all)
 

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

✓ Solution by Mathematica

Time used: 0.010 (sec). Leaf size: 66

DSolve[{t*D[x[t],t]+6*x[t]-y[t]-3*z[t]==0,t*D[y[t],t]+23*x[t]-6*y[t]-9*z[t]==0,t*D[z[t],t]+x[t]+y[t]-2*z[t]==0},{x[t],y[t],z[t]},t,IncludeSingularSolutions -> True]
 

\begin{align*} x(t)\to c_3 t^2+c_2 t+\frac {c_1}{t} \\ y(t)\to -c_3 t^2+c_2 t+\frac {2 c_1}{t} \\ z(t)\to 3 c_3 t^2+2 c_2 t+\frac {c_1}{t} \\ \end{align*}