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Can you please walk me through the problem: Consider the system of differential equations (dx/dt)=−5y and (dy/dt)=−5x Convert this system to a second order differential equation in y by differentiating the second equation with respect to tt and substituting for x from the first equation. Solve the equation you obtained for y as a function of t; hence find x as a function of t. If we also require x(0)=4 and y(0)=1, what are x and y? x(t)=? y(t)=? And please include the steps

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Can you please walk me through the problem: Consider the system of differential

equations

(dx/dt)=−5y               and (dy/dt)=−5x

Convert this system to a second order differential equation in  y by differentiating the second equation with respect to  tt and substituting for  x from the first equation.

Solve the equation you obtained for  y as a function of  t; hence find  x as a function of  t. If we also require x(0)=4 and y(0)=1, what are x and y?

x(t)=?

y(t)=?

And please include the steps

 
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