Question

In: Advanced Math

Use a LaPlace transform to solve d^2x/dt^2+dx/dt+dy/dt=0 d^2y/dt^2+dy/dt-4dy/dt=0 x(0)=1,x'(0)=0 y(0)=-1,y'(0)=5

Use a LaPlace transform to solve

d^2x/dt^2+dx/dt+dy/dt=0

d^2y/dt^2+dy/dt-4dy/dt=0

x(0)=1,x'(0)=0

y(0)=-1,y'(0)=5

Solutions

Expert Solution


Related Solutions

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 ODE (3x - 2y + 1)dx + (-2x + y + 2)dy = 0 with...
Solve ODE (3x - 2y + 1)dx + (-2x + y + 2)dy = 0 with the method of x =u + h and y = v + k
Solve the given initial-value problem. dx/dt = y − 1 dy/dt = −6x + 2y x(0)...
Solve the given initial-value problem. dx/dt = y − 1 dy/dt = −6x + 2y x(0) = 0, y(0) = 0
Initial value problem : Differential equations: dx/dt = x + 2y dy/dt = 2x + y...
Initial value problem : Differential equations: dx/dt = x + 2y dy/dt = 2x + y Initial conditions: x(0) = 0 y(0) = 2 a) Find the solution to this initial value problem (yes, I know, the text says that the solutions are x(t)= e^3t - e^-t and y(x) = e^3t + e^-t and but I want you to derive these solutions yourself using one of the methods we studied in chapter 4) Work this part out on paper to...
d^2y/dx^2 − dy/dx − 3/4 y = 0, y(0) = 1, dy/dx(0) = 0, Convert the...
d^2y/dx^2 − dy/dx − 3/4 y = 0, y(0) = 1, dy/dx(0) = 0, Convert the initial value problem into a set of two coupled first-order initial value problems and find the exact solution to the differential equatiion
Solve the system by Laplace Transform: x'=x-2y y'=5x-y x(0)=-1, y(0)=2
Solve the system by Laplace Transform: x'=x-2y y'=5x-y x(0)=-1, y(0)=2
Use the Laplace transform to solve the problem with initial values y''+2y'-2y=0 y(0)=2 y'(0)=0
Use the Laplace transform to solve the problem with initial values y''+2y'-2y=0 y(0)=2 y'(0)=0
dx/dt = -5x + y , dy/dt = 4x - 2y
dx/dt = -5x + y , dy/dt = 4x - 2y
Use the Laplace transform to solve the problem with initial values y''-2y'+2y=cost y(0)=1 y'(0)=0
Use the Laplace transform to solve the problem with initial values y''-2y'+2y=cost y(0)=1 y'(0)=0
Solve (1+e^x)dy/dx+(e^x)y=3x^2+1 Solve (x^3+y^3)dx+3xy^2 dy = 0 Solve (y-cos y)dx + (xsiny+x)dy = 0 Solve (1+ln...
Solve (1+e^x)dy/dx+(e^x)y=3x^2+1 Solve (x^3+y^3)dx+3xy^2 dy = 0 Solve (y-cos y)dx + (xsiny+x)dy = 0 Solve (1+ln x +y/x)dx = (1-lnx)dy Solve (y^2+yx)dx - x^2dy =0 Solve (x^2+2y^2)dx = xydy Solve Bernoulli's Equation x dy/dx + 2y = (x^4)(e^x)(y^2) Solve Bernoulli's Equation (1+x^2) dy/dx = 2xy +(e^x)(y^2) Solve IVP (3e^(x^2))dy + (xy^2)dx=0 ; y(1) = 2 Solve IVP dy/dx -2xy = e^(x^2) ; y(0)=0 Solve IVP (x^2+y^2)dx+(2xy)dy=0; y(1)=1 6. Mixture Problem Initially 40 lb of salt is dissolved in a large...
ADVERTISEMENT
ADVERTISEMENT
ADVERTISEMENT