Set up the appropriate form of the particular solution to each of the differential equations below,...

Set up the appropriate form of the particular solution to each of the differential equations below, but do NOT determine the values of the coefficients.

(a) y′′ +10y′ +25y=2e^(5t) +te^(−5t)

b) y′′ +9y=5t^2 +4cos(3t)+6e^(3t)

Solutions

Expert Solution

Colby Messinger answered 1 year ago

Next > < Previous

Related Solutions

Determine the form of a particular solution to the following differential equations (do not evaluate coefficients)....

Determine the form of a particular solution to the following differential equations (do not evaluate coefficients). (a)y′′ −4y′ = x+1+ xe^(2x) + e^(4x) + e^(4x)sin4x

1. Determine the form of a particular solution for the following differential equations. (Do not evaluate...

1. Determine the form of a particular solution for the following differential equations. (Do not evaluate the coefficients.) (a) y'' − y' − 6y = x^2 e^x sin x + (2x^3 − 1)e ^ cos x. (b) y'' − y' − 6y = (2 − 3x^3 )e^3x . (c) y'' + 4y' + 4y = x(e^x + e^−x )^2 . (d) y'' − 2y' + 2y = (x − 1)e^x sin x + x^2 e^−x cos x. 2. Find a...

For each of the following differential equations, find the particular solution that satisfies the additional given...

For each of the following differential equations, find the particular solution that satisfies the additional given property (called an initial condition). y'y = x + 1

Determine the reasonable form of the particular solution for each non homogeneous differential equation. Do not...

Determine the reasonable form of the particular solution for each non homogeneous differential equation. Do not solve it. a) y''-y'-2y= e^-x+xcos2x+e^xsin2x. b) D^2[y] +4y =1+x^2+xsin2x.

Find the general solution of the following differential equations (complementary function + particular solution). Find the...

Find the general solution of the following differential equations (complementary function + particular solution). Find the particular solution by inspection or by (6.18), (6.23), or (6.24). Also find a computer solution and reconcile differences if necessary, noticing especially whether the particular solution is in simplest form [see (6.26) and the discussion after (6.15)]. (D2+2D+17)y = 60e−4x sin 5x

Using variation of parameters, find a particular solution of the given differential equations: a.) 2y" +...

Using variation of parameters, find a particular solution of the given differential equations: a.) 2y" + 3y' - 2y = 25e-2t (answer should be: y(t) = 2e-2t (2e5/2 t - 5t - 2) b.) y" - 2y' + 2y = 6 (answer should be: y = 3 + (-3cos(t) + 3sin(t))et ) Please show work!

The SIR Model for the Spread of Disease Set up the three differential equations and perform...

The SIR Model for the Spread of Disease Set up the three differential equations and perform a simulation of the solution of the three equations. Start with a Susceptible (S) of 327,500,000 (the population of the US) and I value of 1 and an R value of zero. Derive your constants, r,a so your simulation matches current values of I and R. Use a dt of 1 day.

1. Set-up the appropriate differential equation(s) and solve to derive the general equation of motion for...

1. Set-up the appropriate differential equation(s) and solve to derive the general equation of motion for a human sized “dummy” moving vertically (up/down) under the following assumptions: (a)The initial elevation is h0 ft. (b)The initial velocity is V0 ft./sec. (c)All motion vertical (ignore any sideways motion). (d)The force due to wind is proportional to velocity and in the opposite direction of velocity. (e)The “terminal velocity” is 120mph (e.g. lim t→∞ (V)= 120 mph). (f)Force = Mass * Acceleration. (g)Acceleration due to...

Solve each system. Express the solution set using vectors. Identify a particular solution and the solution...

Solve each system. Express the solution set using vectors. Identify a particular solution and the solution set of the homogeneous system. (a) 3x + 6y = 18 x + 2y = 6 (b) x + y = 1 x − y = −1 (c) x1 + x3= 4 x1 − x2 + 2x3 = 5 4x1 − x2 + 5x3 = 17 (d) 2a + b − c = 2 2a + c = 3 a − b = 0...

Write down Maxwell’s equations in differential and integral form and explain the physics behind each one...

Write down Maxwell’s equations in differential and integral form and explain the physics behind each one of them. Modify one of them to account for the existence of magnetic monopoles.

Subjects