1. For each of these problems, (i) verify by direct substitution
that y1 and y2 are...
1. For each of these problems, (i) verify by direct substitution
that y1 and y2 are both solutions of the ODE, and (ii) find the
particular solution in the form y(x) = c1y1(x) + c2y2(x) that
satisfies the given initial conditions. (a) y''+5y'-6y=0, y1(x) =
e^−6x , y2(x) = e^x , y(0)=2, y'(0)=1
Find the function y1(t) which is the solution of 4y″+32y′+64y=0
with initial conditions y1(0)=1,y′1(0)=0.
y1(t)=?
Find...
Find the function y1(t) which is the solution of 4y″+32y′+64y=0
with initial conditions y1(0)=1,y′1(0)=0.
y1(t)=?
Find the function y2(t) which is the solution of 4y″+32y′+64y=0
with initial conditions y2(0)=0, y′2(0)=1.
y2(t)= ?
Find the Wronskian of these two solutions you have found:
W(t)=W(y1,y2).
W(t)=?
Find y as a function of x if
x^2y''−17xy'+81y=x^7,
y(1)=−3, y'(1)=4, given that y1=x^9, y2=x^9ln(x) are...
Find y as a function of x if
x^2y''−17xy'+81y=x^7,
y(1)=−3, y'(1)=4, given that y1=x^9, y2=x^9ln(x) are two
solutions to the corresponding homogeneous equation.
1. Let Q1 = x, where (x, y) satisfies that (1)x + (−3)y = −22
(−1)x...
1. Let Q1 = x, where (x, y) satisfies that (1)x + (−3)y = −22
(−1)x + (7)y = 54 . Let Q = ln(3+|Q1|). Then T = 5 sin2 (100Q)
satisfies:— (A) 0 ≤ T < 1. — (B) 1 ≤ T < 2. — (C) 2 ≤ T <
3. — (D) 3 ≤ T < 4. — (E) 4 ≤ T ≤ 5.
2. Let (Q1, Q2) = (x, y), where (x, y) solves x = (7)x...
Let p = (8, 10, 3, 11, 4, 0, 5, 1, 6, 2, 7, 9) and...
Let p = (8, 10, 3, 11, 4, 0, 5, 1, 6, 2, 7, 9) and let q = (2,
4, 9, 5, 10, 6, 11, 7, 0, 8, 1, 3) be tone rows. Verify that p =
Tk(R(I(q))) for some k, and find this value of k.