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
The text passage contains a mathematical question related to solving a system of differential equations using linear algebra. The question is presented, and a method to solve it is partially outlined, but the final answer is not provided.
single_question
Given a text passage, determine:
    1. If it contains a mathematical question (including word problems or calculations)
    2. If an answer to that mathematical question is provided in the text

First, describe the content structure you found in 1-2 sentences.

Then provide your analysis in the following format:
TYPE: <one of the following values>
- NO_QUESTION
- SINGLE_QUESTION
- SINGLE_QUESTION_WITH_ANSWER
- MULTIPLE_QUESTIONS
- MULTIPLE_QUESTIONS_WITH_ANSWERS
system
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
user
The text passage contains a mathematical question related to solving a system of differential equations using linear algebra. The question is presented, and a method to solve it is partially outlined, but the final answer is not provided.

TYPE: SINGLE_QUESTION