Question

Given that ? = ?1 ?x + ?2 ?-x is a two-parameter family of solutions of...

Given that ? = ?1 ?x + ?2 ?-x is a two-parameter family of solutions of ?′′ − ? = 0

on the interval (−∞, ∞), find a member of the family satisfying the initial conditions: ?(0) = −1, ?′(0) = 2.

Homework Answers

Answer #1

In this question using initial condition I have find the member of the family equation.Hope you understand the solution.

Please like

Know the answer?
Your Answer:

Post as a guest

Your Name:

What's your source?

Earn Coins

Coins can be redeemed for fabulous gifts.

Not the answer you're looking for?
Ask your own homework help question
Similar Questions
In this problem, y = c1ex + c2e−x is a two-parameter family of solutions of the...
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
In this problem, y = c1ex + c2e−x  is a two-parameter family of solutions of the second-order...
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) = 8,    y'(−1) = −8 y=
In this problem, x = c1 cos t + c2 sin t is a two-parameter family...
In this problem, x = c1 cos t + c2 sin t is a two-parameter family of solutions of the second-order DE x'' + x = 0. Find a solution of the second-order IVP consisting of this differential equation and the given initial conditions. x(π/6) = 1 2 , x'(π/6) = 0 x=
(a) verfiy that y=tan(x+c) ia a one parameter family of solutions of the differential equation y'=...
(a) verfiy that y=tan(x+c) ia a one parameter family of solutions of the differential equation y'= 1+x^2 (b)since f(x,y)= 1+y^2 and df/dy= 2y are continuous everywhere, the region R can be taken to be the entire xy-plane. Use the family of solutions in part A to find an explicit solution of the first order initial value problem y'= 1+y^2, y(0)=0. Even though x0=0 is in the interval (-2,2) explain why the solution is not defined on its interval (c)determine the...
y = c1 cos(5x) + c2 sin(5x) is a two-parameter family of solutions of the second-order...
y = c1 cos(5x) + c2 sin(5x) is a two-parameter family of solutions of the second-order DE y'' + 25y = 0. If possible, find a solution of the differential equation that satisfies the given side conditions. The conditions specified at two different points are called boundary conditions. (If not possible, enter IMPOSSIBLE.) y(0) = 1, y'(π) = 7 y =
A one parameter family (with parameter cc) of solutions to the problem y′=y−y^2 is y=1/(1+ce−x) Find...
A one parameter family (with parameter cc) of solutions to the problem y′=y−y^2 is y=1/(1+ce−x) Find c so that y(−2)=−3
On page 51 we showed that a one-parameter family of solutions of the first-order differential equation...
On page 51 we showed that a one-parameter family of solutions of the first-order differential equation dy/dx=xy^(1/2) is y=((1/4)x^4+c)^2 for c>=0. Each solution in this family is defined on (-inf,inf). The last statement is not true if we choose c to be negative. For c=-1, explain why y=((1/4)x^4+c)^2 is not a solution of the DE on the interval (-inf,inf). Find an interval of definition I on which y=((1/4)x^4+c)^2 is a solution of the DE.
Verify that the given two-parameter family of functions is the general solution of the non homogeneous...
Verify that the given two-parameter family of functions is the general solution of the non homogeneous differential equation on the indicated interval. y'' + y = sec x y = c1cosx + c2sinx + xsinx + cosxln(cos x) ; (−π/2, π/2)
(a) Use the fact that 5x2 − y2 = c is a one-parameter family of solutions...
(a) Use the fact that 5x2 − y2 = c is a one-parameter family of solutions of the differential equation y dy/dx = 5x to find an implicit solution of the initial-value problem y dy/dx = 5x, y(4) = −10. Then sketch the graph of the explicit solution of this problem. Give the interval I of definition of the explicit solution. (Enter your answer using interval notation.) (b) Are there any explicit solutions of y dy/dx = 5x  that pass through...
B. a non-homogeneous differential equation, a complementary solution, and a particular solution are given. Find a...
B. a non-homogeneous differential equation, a complementary solution, and a particular solution are given. Find a solution satisfying the given initial conditions. y''-2y'-3y=6 y(0)=3 y'(0) = 11 yc= C1e-x+C2e3x yp = -2 C. a third-order homogeneous linear equation and three linearly independent solutions are given. Find a particular solution satisfying the given initial conditions y'''+2y''-y'-2y=0, y(0) =1, y'(0) = 2, y''(0) = 0 y1=ex, y2=e-x,, y3= e-2x
ADVERTISEMENT
Need Online Homework Help?

Get Answers For Free
Most questions answered within 1 hours.

Ask a Question
ADVERTISEMENT