2) Solve the system of equations below dx/dt – 3x – 6y = t^2 ...

2)   Solve the system of equations below
          dx/dt – 3x – 6y = t^2
          dx/dt + dy/dt – 3y = e^t

Expert Solution

Colby Messinger answered 1 year ago

Use the Laplace transform to solve the given system of differential equations. dx/dt + 3x +...

Use the Laplace transform to solve the given system of differential equations. dx/dt + 3x + dy/dt = 1 dx/dt − x + dy/dt − y = e^t x(0) = 0, y(0) = 0

Solve the given system of differential equations by systematic elimination. 2 dx dt − 6x +...

Solve the given system of differential equations by systematic elimination. 2 dx dt − 6x + dy dt = et dx dt − x + dy dt = 3et

Use the Laplace transform to solve the given system of differential equations. dx/dt + 2x +dy/dt=...

Use the Laplace transform to solve the given system of differential equations. dx/dt + 2x +dy/dt= 1 dx/dt− x+ dy/dt− y= e^t x(0) = 0, y(0) = 0

Solve the system of equations: x+y^2=6y x-2y=-5

Assume x and y are functions of t. Evaluate dy/dt with 4xy-5x+6y^3=-126, with dx/dt=-18, and x=6,y=-2...

Assume x and y are functions of t. Evaluate dy/dt with 4xy-5x+6y^3=-126, with dx/dt=-18, and x=6,y=-2 A retail store estimates that weekly sales and weekly advertising costs x are related by s=50,000-30,000e^-0.0004x. The current weekly advertising costs are $2,500, and these costs are increasing at a rate of $400 per week. Find the current rate of change of sales per week. Use implicit differentiation to find y’ for the equation below and then evaluate y’ at the indicated point, (-4,4)....

Solve the system of equation by method of elimination. dx/dt + x−5y = 0, 4x +dy/dt+...

Solve the system of equation by method of elimination. dx/dt + x−5y = 0, 4x +dy/dt+ 5y = 0, x(0) = −1, y(0) = 2.

solve the SDE dX = − 1 /τ( (X − µ)dt) + (2D)-1/2 dB. X(t =...

solve the SDE dX = − 1 /τ( (X − µ)dt) + (2D)-1/2 dB. X(t = 0) = β

($4.6 Variation of Parameters): Solve the equations (a)–(c) using method of variation of parameters. (a) y''-6y+9y=8xe^3x...

($4.6 Variation of Parameters): Solve the equations (a)–(c) using method of variation of parameters. (a) y''-6y+9y=8xe^3x (b) y''-2y'+2y=e^x (secx) (c) y''-2y'+y= (e^x)/x

Use Laplace transformations to solve the following differential equations: dy(t)/dt + a y(t) = b; I.C.s...

Use Laplace transformations to solve the following differential equations: dy(t)/dt + a y(t) = b; I.C.s y(0) = c d2y(t)/dt2 + 6 dy(t)/dt + 9 y(t) = 0; I.C.s y(0) = 2, dy(0)/dt = 1 d2y(t)/dt2 + 4 dy(t)/dt + 8 y(t) = 0; I.C.s y(0) = 2, dy(0)/dt = 1 d2y(t)/dt2 + 2 dy(t)/dt + y(t) = 3e-2t; I.C.s y(0) = 1, dy(0)/dt = 1

Use variation of parameters to solve the following differential equations y''-5y'-6y=tln(t)

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