(16 points) Find y as a function of a if y" + 16y' = 0, y(0) = -7, y(0) = 12, 7(0) = 48. y(x) =
(1 point) Find yy as a function of xx ify′′′+64y′=0,y‴+64y′=0,y(0)=−1, y′(0)=−16, y′′(0)=−192.y(0)=−1, y′(0)=−16, y″(0)=−192.y(x)=
(17 points) Find y as a function of x if y" – 7y" — y' + 7y = 0, y(0) = -9, y'(0) = 2, y" (O) = 87. y(x) =
Solve 2y'' – 5y' – 25y = 0, y(0) = -6, y'(0) = – 15 (t) = Consider the initial value problem y' + 3y' – 10y = 0, y(0) = a, y'(0) = 3 Find the value of a so that the solution to the initial value problem approaches zero as t + oo a = 1
1. (25 points) Consider the following probability density function and the random vector W. fxy(x,y)= 1/16 0 |x|52, lyls2 elsewhere X W=(x,y)" Li a) (5 points) Find and plot the conditional joint probability density function f wilx<0,y>o)(W|x<0, y>0) b) (5 points) Find and plot the conditional joint cumulative distribution function Fw1(x<0,y>0)(W|x<0, y>0) c) (5 points) Find E(W). d) (10 points) Find E(W x<0, y>0).
(1 point) Solve the boundary-value problem y" – 10y' + 25y = 0, y(0) = 7, y(1) = 0. Answer: y(x) = Note: If there is no solution, type "None".
Q5) Find a general solution. Check your answer by substitution. 4y" – 25y = 0 y" + 36y = 0 y" + 6y' + 8.96y = 0) y" + 2k%y' + k4y = 0 Q6) Solve the IVP. Check that your answer satisfies the ODE as well as the initial conditions. Show the details of your work. y" + 25y = 0, y(0) = 4.6, y'(0) = -1.2 4y" – 4y' – 3y = 0, y(-2) = e, y'(-2) =...
[-/1.25 Points] DETAILS ZILLDIFFEQMODAP11 4.2.007. The indicated function y(x) is a solution of the given differential equation. Use reduction of order or formula (5) in Section 4.2, e-P(x) dx r2 = y g(x) / dx (5) as instructed, to find a second solution v2(X). Ay" - 20y + 25y = 0; Y-S/2 Y2 Need Help?
(1 point) Find the general solution to y + 8y" + 25y' = 0. In your answer, use c. and.cy to denote arbitrary constants and the independent variable. help (equations)
2. Find the general solution to y(4) -4y" +14y" +44y+25y 0 3. Find the general solution to y" +y-sin r