Question

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 =

Homework Answers

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, 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=
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, 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
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)
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.
1) The given family of functions is the general solution of the differential equation on the...
1) The given family of functions is the general solution of the differential equation on the indicated interval. Find a member of the family that is a solution of the initial-value problem. y = c1 + c2 cos(x) + c3 sin(x), (−∞, ∞); y''' + y' = 0,    y(π) = 0,    y'(π) = 8,    y''(π) = −1 y = 2) Two chemicals A and B are combined to form a chemical C. The rate, or velocity, of the reaction is proportional to the...
(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...
1.Solve sin(x)=−0.61sin(x)=-0.61 on 0≤x<2π0≤x<2πThere are two solutions, A and B, with A < B 2.Solve 5cos(5x)=25cos(5x)=2...
1.Solve sin(x)=−0.61sin(x)=-0.61 on 0≤x<2π0≤x<2πThere are two solutions, A and B, with A < B 2.Solve 5cos(5x)=25cos(5x)=2 for the smallest three positive solutions.Give your answers accurate to at least two decimal places, as a list separated by commas 3.Solve 5sin(π4x)=35sin(π4x)=3 for the four smallest positive solutions 4.Solve for tt, 0≤t<2π0≤t<2π 21sin(t)cos(t)=9sin(t)21sin(t)cos(t)=9sin(t) 5.Solve for the exact solutions in the interval [0,2π)[0,2π). If the equation has no solutions, respond with DNE. 2sec2(x)=3−tan(x) 6.Give the smallest two solutions of sin(7θθ) = -0.6942 on [...
DIFFERENTIAL EQUATIONS 1. A force of 400 newtons stretches a spring 2 meters. A mass of...
DIFFERENTIAL EQUATIONS 1. A force of 400 newtons stretches a spring 2 meters. A mass of 50 kilograms is attached to the end of the spring and is initially released from the equilibrium position with an upward velocity of 10 m/s. Find the equation of motion. 2. A 4-foot spring measures 8 feet long after a mass weighing 8 pounds is attached to it. The medium through which the mass moves offers a damping force numerically equal to times the...