Question Type 2: Finding the particular solution to linear coupled differential equations with some initial condition and real and distinct eigenvalues Exercises

Find the particular solution of the decoupled system

with $x(0)=4$, $y(0)=2$.

Solve the initial value problem

with $x(0)=4$, $y(0)=2$.

Find $x(t)$ and $y(t)$ if

and $x(0)=4$, $y(0)=2$.

Solve for $x(t)$ and $y(t)$ in the system

with $x(0)=4$, $y(0)=2$.

Determine $x(t)$ and $y(t)$ for

with $x(0)=4$, $y(0)=2$.

Find the particular solution of the system

with initial conditions $x(0)=4$, $y(0)=2$.

Find the particular solution of

with $x(0)=4$, $y(0)=2$.

Solve the system

with $x(0)=4$, $y(0)=2$.

Find the particular solution of

with $x(0)=4$, $y(0)=2$.

Determine the particular solution to

with $x(0)=4$, $y(0)=2$.

Determine $x(t)$ and $y(t)$ for

with $x(0)=4$, $y(0)=2$.

Solve

with $x(0)=4$, $y(0)=2$.