Question

Find the solution to the linear system of differential equations \begin{cases} x' = -3x \\ y' = -12x + 3y \end{cases} satisfying the initial conditions $x(0) = -3$ and $y(0) = -5$. $x(t) =$ $y(t) = $

          Find the solution to the linear system of differential equations \begin{cases} x' = -3x \\ y' = -12x + 3y \end{cases} satisfying the initial conditions $x(0) = -3$ and $y(0) = -5$.

$x(t) =$

$y(t) = $

Find the solution to the linear system of differential equations x' = -3x
y' = -12x + 3y satisfying the initial conditions x(0) = -3 and y(0) = -5.

x(t) =

y(t) =

Added by Andrew R.

Calculus: Early Transcendentals

James Stewart 8th Edition

Instant Answer

Solved by Expert Carson Merrill

Step 1

This is a separable differential equation, so we can separate the variables and integrate both sides: 1/x dx = -3 dt Integrating both sides gives: ln|x| = -3t + C1 where C1 is the constant of integration. Exponentiating both sides gives: |x| = e^(-3t + Show more…

Show all steps

Thanks for your feedback!

Find the solution to the linear system of differential equations {xâ€²=âˆ’3x, yâ€²=âˆ’12x+3y} satisfying the initial conditions x(0)=âˆ’3 and y(0)=âˆ’5. x(t)= y(t)= -3x satisfying the initial conditions -12x+3y Find the solution to the linear system of differential equations xâ€²=âˆ’3x, yâ€²=âˆ’12x+3y satisfying the initial conditions x(0)=âˆ’3 and y(0)=âˆ’5. x(t)= y(t)=