Solve the following systems of differential equations by eli

Solve the following systems of differential equations by elimination and Laplace transform methods: {y + x\' = 0 x(0) = y(0) = 2 y\'-2x-2y = 0 {x\' = y - z, y\' = y + x, x(0) = 2, y(0) = 3, z(0) = 4 z\' = x + z

Solution

B.SX¹(S)-X¹(0)=X¹(S)-1/S

SY¹(S)-Y¹(0)=Y¹(S)-1/S²

SZ¹(S)-Z¹(0)=Z¹(S)-1/S³

^{now plug in the initial conditions and siple things a list}

^{x1(s)=3/s-4solving of x₁}(s)

y₁(s)=3s+2/s

z₁(s)=2s+4/s