2 -e Recall that cosh(x) er te 2 and sinh(2) Any general solution of y'' –...
Recall three facts about hyperbolic cosine and hyperbolic sine functions: dr cosh(x) = sinh(x), di sinh(x) = cosh(x), cosh? (x) – sinh? (x) = 1. Compute the Wronskian of cosh(2) and sinh(2). Using your question 1's answer, cosh() and sinh(x) are linearly independent on R True False
Please solve all three. Thank you very much 5. (a) Let a be a constant (we can write “a ER” to mean “a is a real number”). Verify that y(x) = ci cos(ax) + C2 sin(ax) is a solution for y" = -a’y, where C1,C2 ER. (b) Consider the hyperbolic trigonometric functions defined by cosh(x) = et tex 2 ex – e- sinh(x) = * d Show that I cosh(x) = sinh(x) and sinh(x) = cosh(x). (e) Verify that y(x)...
(3 points) (a) Find the general solution to y′′+2y′=0. Give your answer as y=... . In your answer, use c1 and c2 to denote arbitrary constants and x the independent variable. Enter c1 as c1 and c2 as c2. (3 points) (a) Find the general solution to y" + 2y' = 0. Give your answer as y=... . In your answer, use c1 and c2 to denote arbitrary constants and x the independent variable. Enter cı as c1 and C2...
1 point) (a) Find the general solution to y" +7y'-0. Give your answer as y -.. . In your answer, use ci and c2 to denote arbitrary constants and x the independent variable. Enter ci as c1 and c as c2 help (equations) (b) Find the particular solution that satisfies y(0) 1 and y'(0)1 help (equations)
The answer above is NOT correct. (1 point) Find the general solution to y(4) – 8y"" + 15y" = 0. In your answer, use C1,C2,C3 and C4 to denote arbitrary constants and x the independent variable. Enter ci as c1, c2 as c2, etc. y=c1+xc1+c3e^(3x)+c4e^(5x) help (equations)
Consider the differential equation: y' - 5y = -2x – 4. a. Find the general solution to the corresponding homogeneous equation. In your answer, use cı and ca to denote arbitrary constants. Enter ci as c1 and ca as c2. Yc = cle cle5x - + c2 b. Apply the method of undetermined coefficients to find a particular solution. yp er c. Solve the initial value problem corresponding to the initial conditions y(0) = 6 and y(0) = 7. Give...
(a) Find the general solution to y''-10y'+25y=0. Enter your answer as y = .... In your answer, use c1 and c2 to denote arbitrary constants and x the independent variable. Enter c1 as c1 and c2 as c2.(b) Find the solution that satisfies the initial conditions y(0)=4 and y'(0)=0.
Find the general solution, y(t), of the differential equation t y" – 5ty' +9y=0, t> 0. Below C1 and C2 are arbitrary constants.
Find the general solution to y'' + 8y' + 41y = 0. Give your answer as y=.... In your answer, use c1 and c2 to denote arbitrary constants and the independent variable.
Find the general solution of the differential equation. Use C1 and C2 to denote any arbitrary constants. 1) y'(t) = y(4t3 + 1) 3) y'(t) = 18t5 – 10t4 + 8 – 2t-2 4) y"(t) = 40e5t + sin(4t)