Question

In: Math

Verify that the indicated family of functions is a solution of the given differential equation. Assume...

Verify that the indicated family of functions is a solution of the given differential equation. Assume an appropriate interval I of definition for each solution.

d^2y/ dx^2 − 6 dy/dx + 9y = 0;    y = c1e3x + c2xe3x  When y = c1e3x + c2xe3x,

dy
dx
=
d2y
dx2
=   .


Thus, in terms of x,

d^2y/dx^2− 6 dy/dx + 9y =

+ 9(c1e3x + c2xe3x)
=   .

2) In this problem, y = c1ex + c2e−x is a two-parameter family of solutions of the second-order DE

y'' − y = 0. Find a solution of the second-order IVP consisting of this differential equation and the given initial conditions.

y(−1) = 7,    y'(−1) = −7

y =

Solutions

Expert Solution

milcah answered 2 years ago
Next > < Previous

Related Solutions

Use direct substitution to verify that y(t) is a solution of the given differential equation in...
Use direct substitution to verify that y(t) is a solution of the given differential equation in Exercise Group 1.1.9.15–20. Then use the initial conditions to determine the constants C or c1 and c2. 17. y′′+4y=0, y(0)=1, y′(0)=0, y(t)=c1cos2t+c2sin2t 18. y′′−5y′+4y=0,   y(0)=1 , y′(0)=0,   y(t)=c1et+c2e4t 19. y′′+4y′+13y=0, y(0)=1, y′(0)=0, y(t)=c1e−2tcos3t+c2e−3tsin3t 27. The growth of a population of rabbits with unlimited resources and space can be modeled by the exponential growth equation, dP/dt=kP. Write a differential equation to model a population of...
The indicated function y1(x) is a solution of the given differential equation. Use reduction of order...
The indicated function y1(x) is a solution of the given differential equation. Use reduction of order to find y2(x) x2y'' − xy' + 17y = 0 ;   y1=xsin(4In(x))
The indicated function y1(x) is a solution of the given differential equation. Use reduction of order...
The indicated function y1(x) is a solution of the given differential equation. Use reduction of order or formula (5) in Section 4.2, y2 = y1(x) e−∫P(x) dx y 2 1 (x) dx (5) as instructed, to find a second solution y2(x). x2y'' − xy' + 26y = 0; y1 = x sin(5 ln(x)).......................................
Given the complementary solution and the differential equation, Give the particular and the total solution for...
Given the complementary solution and the differential equation, Give the particular and the total solution for the initial conditions. Use C1 and C2 for the weights, where C1 is associated with the root with smaller magnitude. If the roots are complex, the complementary solution is the weighted sum of complex conjugate exponentials, which can be written as a constant times a decaying exponential times a cosine with phase. Use C1 for the constant and Phi for the phase. (Note: Some...
Topic: Differential Equations; reduction order. The indicated fuction y1(x) is a solution of the given differential...
Topic: Differential Equations; reduction order. The indicated fuction y1(x) is a solution of the given differential equation. Use the reduction order technique to find a second solution y2(x). xy'' + y' = 0;    y1= ln(x) Please, explain deeply each part of the solution, and include complete algebraic explanation as well. Otherwise, the answer will be negatively replied.
Partial Differential Equations (a) Find the general solution to the given partial differential equation and (b)...
Partial Differential Equations (a) Find the general solution to the given partial differential equation and (b) use it to find the solution satisfying the given initial data. Exercise 1. 2∂u ∂x − ∂u ∂y = (x + y)u u(x, x) = e −x 2 Exercise 2. ∂u ∂x = −(2x + y) ∂u ∂y u(0, y) = 1 + y 2 Exercise 3. y ∂u ∂x + x ∂u ∂y = 0 u(x, 0) = x 4 Exercise 4. ∂u...
Use the one solution given below to find the general solution of the differential equation below...
Use the one solution given below to find the general solution of the differential equation below by reduction of order method: (1 - 2x) y'' + 2y' + (2x - 3) y = 0 One solution: y1 = ex
Find a particular solution of the given differential equation. Use a CAS as an aid in...
Find a particular solution of the given differential equation. Use a CAS as an aid in carrying out differentiations, simplifications, and algebra. y(4) + 2y'' + y = 11 cos(x) − 12x sin(x)
Find the general solution of the given differential equation, and use it to determine how solutions...
Find the general solution of the given differential equation, and use it to determine how solutions behave as t→∞. 9y′+y=5t2
find the general solution of the given differential equation. 1. y'' + y = tan t,...
find the general solution of the given differential equation. 1. y'' + y = tan t, 0 < t < π/2 2. y'' + 4y' + 4y = t-2 e-2t , t > 0 find the solution of the given initial value problem. 3. y'' + y' − 2y = 2t, y(0) = 0, y'(0) = 1
ADVERTISEMENT
Subjects
ADVERTISEMENT
Latest Questions
ADVERTISEMENT