Consider the differential equation 2y^2+10y+12 = t+e^t Find the complementary function and particular integral. Hence write...

Consider the differential equation

2y^2+10y+12 = t+e^t

Find the complementary function and particular integral. Hence write down the full general solution

Solutions

Expert Solution

Colby Messinger answered 1 year ago

Next > < Previous

Related Solutions

Find the particular integral of the differential equation d2y/dx2 + 3dy/dx + 2y = e −2x...

Find the particular integral of the differential equation d2y/dx2 + 3dy/dx + 2y = e −2x (x + 1). show that the answer is yp(x) = −e −2x ( 1/2 x2 + 2x + 2) ]

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

Consider the differential equation y '' − 2y ' + 10y = 0; ex cos(3x), ex sin(3x),...

Consider the differential equation y '' − 2y ' + 10y = 0; ex cos(3x), ex sin(3x), (−∞, ∞). Verify that the given functions form a fundamental set of solutions of the differential equation on the indicated interval. The functions satisfy the differential equation and are linearly independent since W(ex cos(3x), ex sin(3x)) = _____ANSWER HERE______ ≠ 0 for −∞ < x < ∞. Form the general solution. y = ____ANSWER HERE_____

5. Consider the differential equation xy^5/2 +1+x^2y^3/2dy/dx =0 (a) Show that this differential equation is not...

5. Consider the differential equation xy^5/2 +1+x^2y^3/2dy/dx =0 (a) Show that this differential equation is not exact. (b) Find a value for the constant a such that, when you multiply the d.e. through by xa, it becomes exact. Show your working. Do NOT solve the resulting differential equation. 6. Consider the differential equation (D − 3)(D − 4)y = 0. (a) Solve this d.e., showing brief working. (b) How many solutions does this d.e. have? Justify your answer. (c) How...

Find the general solution of the differential equation y′′+36y=13sec^2(6t), 0<t<π/12.

Consider a nonhomogeneous differential equation ?′′ + 2?′ + ? = 2? sin? (a) Find any...

Consider a nonhomogeneous differential equation ?′′ + 2?′ + ? = 2? sin? (a) Find any particular solution ?? by using the method of undetermined coefficients. (b) Find the general solution. (c) Find the particular solution if ?(0) = 0 and ?′(0) = 0.

Find general solution to the differential equation x'(t) = Ax(t) + v, A = [ 2...

Find general solution to the differential equation x'(t) = Ax(t) + v, A = [ 2 −2; 2 2] , v = (2 0) .

Find the particular solution to the equation. y''-4y'+5y=(e^(2t))(sec(t))

A system is described by the differential equation −5y′′(t)−3y′(t)+3y(t)=ys(t), Find the transfer function associated with this...

A system is described by the differential equation −5y′′(t)−3y′(t)+3y(t)=ys(t), Find the transfer function associated with this system H(s). Write the solution as a single fraction in s. H(s)=_______________?

find a particular solution to y"-2y'+y=-12.5e^t

Subjects