Find the solution to this linear, second order, homogeneous, constant coefficient differential equation: 4y" + 12y'...

Question

Question

Answer 1

Answer #1

4 y +12ytgyzo - Let y = emx be a solution of . y= mema y=ma em so from 0, 4ma ema tiam emxtgem ao = (4m² +12m +9) enx =o

Answer 2

Similar Homework Help Questions

Write a second order, constant-coefficient, homogeneous, linear differential equation in y which has a single critical...

Write a second order, constant-coefficient, homogeneous, linear differential equation in y which has a single critical point y = 0 and for which the phase portrait is a spiral source. y+
Find the general solution of the second order constant coeﬃcient linear ODEs 7. Find the general...

Find the general solution of the second order constant coeﬃcient linear ODEs 7. Find the general solution of the second order constant coefficient linear ODE. (a) y" +2y = 0 (b) 2y" – 3y +y=0 (c) y" – 2y – 2y = 0 (d) y" – 2y + 2y = 0 (e) y" + 2y - 8y = 0 (f) y" +9y=0 (g) y" – 4y + 4y = 0 (h) 25y" – 10y' +y=0
Find a second order homogeneous linear differential equation whose general solution is A tan x +...

Find a second order homogeneous linear differential equation whose general solution is A tan x + B sin x (A, B constant). [Hint: Use the fact that tan x and sin x are, individually, solutions and solve for the coefficients in standard form.]

Find a constant coefficient linear second-order differential equation whose general solution is: y=(c1 + c2(x))e^-3x

Find a constant coefficient linear second-order differential equation whose general solution is: y=(c1 + c2(x))e^-3x
(17 points) A 9th order, linear, homogeneous, constant coefficient differential equation has a characteristic equation which...

(17 points) A 9th order, linear, homogeneous, constant coefficient differential equation has a characteristic equation which factors as follows. (r? - 4r +13)*r(r + 3) = 0 Write the nine fundamental solutions to the differential equation. 99 (You can enter your answers in any order.)
2. You can use Dand write an operator instead of an equation in this question. (a) Find a constant coefficient linear homogeneous differential equation of lowest order that has n(x)-x , y2(z) = x2 ,...

2. You can use Dand write an operator instead of an equation in this question. (a) Find a constant coefficient linear homogeneous differential equation of lowest order that has n(x)-x , y2(z) = x2 , and y3(z) = eェamong its solutions. (b) Now find a different linear homogeneous differential equation of an order lower than the one in (a) that has the same y1,U2,U3 among its solutions. (c) Find a constant coefficient linear homogeneous differential equation of lowest order that...

Find a second order homogeneous linear differential equation whose general equation is Atanx + Bsinx (A,...

Find a second order homogeneous linear differential equation whose general equation is Atanx + Bsinx (A, B constant) [Hint use the fact that tanx and sinx are, individually, solutions and solve for the coefficients in standard form}
(17 points) A 9th order, linear, homogeneous, constant coefficient differential equation has a characteristic equation which...

(17 points) A 9th order, linear, homogeneous, constant coefficient differential equation has a characteristic equation which factors as follows. (P2 - 2r+2) rtr + 3) = 0 Write the nine fundamental solutions to the differential equation. y y2 > Y4= Ys = Y y = 19 = (You can enter your answers in any order.)
(17 points) A 9th order, linear, homogeneous, constant coefficient differential equation has a characteristic equation which...

(17 points) A 9th order, linear, homogeneous, constant coefficient differential equation has a characteristic equation which factors as follows. (p2 + 6r + 18)ºr(r + 1)2 = 0 Write the nine fundamental solutions to the differential equation. Y1 = = Y2 = Y3 Y4 = Y5 = Y6 = = Y7 = Y8 = Y9 =

(17 points) A 9th order, linear, homogeneous, constant coefficient differential equation has a characteristic equation which...

(17 points) A 9th order, linear, homogeneous, constant coefficient differential equation has a characteristic equation which factors as follows. (p2 + 4r + 8) ºr(r – 2)2 = 0 Write the nine fundamental solutions to the differential equation. Y1 = Y2 = Y3 = Y4 = Y5 = Y6 = 47 = Ys = Y9 = (You can enter your answers in any order.)