Solving for x1 and x2 in a system of coupled differential equations

[goodname]

can we solve x1 and x2 using the below quations? if so how?

4(dx1/dt)+5(x1)-2(dx2/dt)=10

-2(dx1/dt)+5(x2)-4(dx2/dt)=0

 

[vela]

Start by solving for dx₁/dt and dx₂/dt in terms of x₁ and x₂. Then use the substitution u(t) = x(t)-2 to get rid of the constant terms. You should end up with

$$\begin{pmatrix}\dot{u}(t) \\ \dot{x}_2(t)\end{pmatrix} = \begin{pmatrix} -1 & 1/2 \\ 1/2 & 1 \end{pmatrix}\begin{pmatrix} u(t) \\ x_2(t) \end{pmatrix}$$

You can solve that system using the usual methods.

 

[goodname]

sorry, i cannot understand..

 

[vela]

Well, as per the forum rules, you need to show some effort at trying to solve the problem on your own. Start by solving for dx₁/dt and dx₂/dt in terms of x₁ and x₂. In other words, find the constants a, b, c, d, e, and f such that

$$\begin{align*}<br /> \frac{dx_1}{dt} &= a x_1 + b x_2 + e \\<br /> \frac{dx_2}{dt} &= c x_1 + d x_2 + f<br /> \end{align*}$$