text: Matrix A:
  1 1
  4 1
  
  x' = Ax
  
  ( x' = Derivative of x )
  
  Solve for the general solution to the system.
  
  Above is the equation. I'm 90% sure it's linear algebra and supposedly a rather simple equation, however I've no idea how to do it as I've not taken linear algebra yet. Bit desperate for an answer to it, any help would be greatly appreciated!
  
  2. Originally Posted by t16
  Matrix A:
  1 1
  4 1
  
  x' = Ax
  
  ( x' = Derivative of x )
  
  Solve for the general solution to the system.
  
  Above is the equation. I'm 90% sure it's linear algebra and supposedly a rather simple equation, however I've no idea how to do it as I've not taken linear algebra yet. Bit desperate for an answer to it, any help would be greatly appreciated!
  Let:
  
  $\displaystyle x={x_1 \brack n_2}$,
  
  then we have a pair of coupled ODEs:
  
  $\displaystyle x_1'=x_1+x_2$
  
  $\displaystyle x_2'=4x_1+x_2$
  
  Differentiate the first equation again to get:
  
  $\displaystyle x_1''=x_1'+x_2'=x_1'+4x_1+x_2=2x_1'+3x_1$
  
  which is a homogeneous linear 2nd order ODE which you should be able to solve for $\displaystyle x_1$.
  
  Now do the same to get the 2nd order ODE for $\displaystyle x_2$.
  
  RonL
explanation: The document contains a math question related to solving a system of differential equations using linear algebra. The question is presented in a forum post format, and it includes a detailed problem statement and a request for help. The document also contains an answer that provides a step-by-step approach to solving the system of differential equations.
distilabel_metadata.content: Evaluate the user given text extract and determine if it contains a math question and optionally and answer to this question.
  
  Output rules:
  
  1. Briefly describe the document and mention if it contains a question or a question and answer.
  2. Finalize the output with: Label: no-question,question,question-and-answer,multiple-question,multiple-question-and-answer
distilabel_metadata.role: system
distilabel_metadata.content: Matrix A:
  1 1
  4 1
  
  x' = Ax
  
  ( x' = Derivative of x )
  
  Solve for the general solution to the system.
  
  Above is the equation. I'm 90% sure it's linear algebra and supposedly a rather simple equation, however I've no idea how to do it as I've not taken linear algebra yet. Bit desperate for an answer to it, any help would be greatly appreciated!
  
  2. Originally Posted by t16
  Matrix A:
  1 1
  4 1
  
  x' = Ax
  
  ( x' = Derivative of x )
  
  Solve for the general solution to the system.
  
  Above is the equation. I'm 90% sure it's linear algebra and supposedly a rather simple equation, however I've no idea how to do it as I've not taken linear algebra yet. Bit desperate for an answer to it, any help would be greatly appreciated!
  Let:
  
  $\displaystyle x={x_1 \brack n_2}$,
  
  then we have a pair of coupled ODEs:
  
  $\displaystyle x_1'=x_1+x_2$
  
  $\displaystyle x_2'=4x_1+x_2$
  
  Differentiate the first equation again to get:
  
  $\displaystyle x_1''=x_1'+x_2'=x_1'+4x_1+x_2=2x_1'+3x_1$
  
  which is a homogeneous linear 2nd order ODE which you should be able to solve for $\displaystyle x_1$.
  
  Now do the same to get the 2nd order ODE for $\displaystyle x_2$.
  
  RonL
distilabel_metadata.role: user
distilabel_metadata.raw_output_q_a_detector_0: The document contains a math question related to solving a system of differential equations using linear algebra. The question is presented in a forum post format, and it includes a detailed problem statement and a request for help. The document also contains an answer that provides a step-by-step approach to solving the system of differential equations.
  
  Label: question-and-answer