Решить систему однородных дифференциальных уравнений

Решите задачу:

$\begin{cases}x'(t)=3x(t)+4y(t)-3z(t)\\y'(t)=x(t)+4y(t)-z(t)\\z'(t)=x(t)+4y(t)-z(t)\end{cases}\\y'(t)=z'(t)\\y'(t)=x(t)+4y(t)-z(t)\\x(t)=y'(t)-4y(t)+z(t)\\x'(t)=y''(t)-4y'(t)+z'(t)\\\\y''(t)-4y'(t)+z'(t)=3y'(t)-12y(t)+3z(t)+4y(t)-3z(t)\\y''(t)-3y'(t)=3y'(t)-8y(t)\\y''(t)-6y'(t)+8y(t)=0\\\lambda^2-6\lambda+8=0\\\lambda_1=2\ \lambda_2=4\\y(t)=z(t)=C_1e^{2t}+C_2e^{4t}\\y'(t)=2C_1e^{2t}+4C_2e^{4t}\\y''(t)=4C_1e^{2t}+16C_2e^{4t}\\\\x'(t)=y''(t)-3y'(t)\\x'(t)=4C_1e^{2t}+16C_2e^{4t}-6C_1e^{2t}-12C_2e^{4t}$
$x'(t)=-2C_1e^{2t}+4C_2e^{4t}\\x(t)=-C_1e^{2t}+C_2e^{4t}\\\\\\\\\begin{cases}x(t)=-C_1e^{2t}+C_2e^{4t}\\y(t)=C_1e^{2t}+C_2e^{4t}\\z(t)=C_1e^{2t}+C_2e^{4t}\end{cases}$