Answers>Further Mathematics>A Level>Article

Find the general solution to: d^(2)x/dt^(2) + 7 dx/dt + 12x = 2e^(-t)

"General Solution = Complimentary Function + Particular Integral"AE: m² + 7m + 12 = 0 solve for m(m+3)=0m = -4 or -3Hence the Complimentary Function = Ae^-4t + Be^-3t
PI: [substitute u=ke^-t]u'=-ke^-tu''=ke^-t[Comparing coefficients we get:]k-7k+12k=2Hence, k = 1/3.PI = 1/3 * e^-tSo the general solution is:x=Ae^-4t + Be^-3t+ 1/3 * e^-t

Answered by Edward O. • Further Mathematics tutor

3938 Views

Find the general solution to: d^(2)x/dt^(2) + 7 dx/dt + 12x = 2e^(-t)

Related Further Mathematics A Level answers

Find the determinant of matrix M. [3]

You are given a polynomial f, where f(x)=x^4 - 14x^3 + 74 x^2 -184x + 208, you are told that f(5+i)=0. Express f as the product of two quadratic polynomials and state all roots of f.

A particle is launched from the top of a cliff of height 87.5m at time t=0 with initial velocity 14m/s at 30 deg above the horizontal, Calculate: a) maximum height reached above bottom of cliff; b)horizontal distance travelled before hitting the ground.

Given that z = a + bj, find Re(z/z) and Im(z/z).

Find the general solution to: d^(2)x/dt^(2) + 7 dx/dt + 12x = 2e^(-t)

Related Further Mathematics A Level answers

Find the determinant of matrix M. [3]

You are given a polynomial f, where f(x)=x^4 - 14x^3 + 74 x^2 -184x + 208, you are told that f(5+i)=0. Express f as the product of two quadratic polynomials and state all roots of f.

A particle is launched from the top of a cliff of height 87.5m at time t=0 with initial velocity 14m/s at 30 deg above the horizontal, Calculate: a) maximum height reached above bottom of cliff; b)horizontal distance travelled before hitting the ground.

Given that z = a + bj, find Re(z/z*) and Im(z/z*).

Given that z = a + bj, find Re(z/z) and Im(z/z).