Systems of differential equations

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Problem: Solve the system of differential equations, using the operational method. \[ \left\{\begin{array}{l} \dot{x}=2 x+8 y \\ \dot{y}=3 x+4 y, \quad x(0)=0, \quad y(0)=2 . \end{array}\right. \]

8.2.2.1 Systems of differential equations

2.57 $

Problem: Solve the inhomogeneous system of differential equations, using the operational method. \[ \left\{\begin{array}{ll} x_{1}^{\prime}=5 x_{1}-18 x_{2}-28 e^{-t} & x_{1}(0)=-1 \\ x_{2}^{\prime}=2 x_{1}-7 x_{2}-9 e^{-t} & x_{2}(0)=-2 \end{array}\right. \]

8.2.2.2 Systems of differential equations

3.85 $

Problem: Solve the inhomogeneous system of differential equations, applying the operational method. \[ \left\{\begin{array}{cc} x_{1}^{\prime}=4 x_{1}-16 x_{2}+11 x_{3}-10 & x_{1}(0)=5 \\ x_{2}^{\prime}=-3 x_{1}+9 x_{2}-7 x_{3}+8, & x_{2}(0)=0 \\ x_{3}^{\prime}=-6 x_{1}+20 x_{2}-15 x_{3}+16 & x_{3}(0)=-1 \end{array}\right. \]

8.2.2.3 Systems of differential equations

3.85 $

Problem: Solve the system of differential equations, using the operational method: \[ \left\{\begin{array}{l} y^{\prime}+5 y-2 x=e^{t} \\ x^{\prime}-y+6 x=e^{-2 t}, \quad x(0)=0, \quad y(0)=0 . \end{array}\right. \]

8.2.2.4 Systems of differential equations

3.85 $

Problem: Solve the Cauchy problem for the system of linear differential equations, using the operational method: \[ \begin{array}{l} 2 x^{\prime \prime}+x-y^{\prime}=-3 \sin t, x+y^{\prime}=-\sin t, \\ x(0)=0, x^{\prime}(0)=1, y(0)=0 . \end{array} \]

8.2.2.5 Systems of differential equations

2.57 $

Problem: Solve the system of differential equations using the operational method: \[ \left\{\begin{array}{l} \dot{x}=x+2 y+1-t-2 e^{3 t} \\ \dot{y}=2 x+3 y-2 t \end{array} x(0)=0, \quad y(0)=1 .\right. \]

8.2.2.6 Systems of differential equations

2.06 $