Differential Equations Answers

1. A mass of 250 g stretches a spring 1.568 cm. If the mass is set in motion from its equilibrium position with a downward velocity of 20 cms, and if there is no damping, determine the position u of the mass at any time t.

Enclose arguments of functions in parentheses. For example, sin(2x).

a. Assume g = 9.8 m/s^2. Enter ans exact answer.
u(t) = ______ m

b. When does the mass first return to its equilibrium position?
Enter an exact answer.

t = ______s

1. Find the solution of the initial value problem y′′+4y=t^2+6e^t, y(0)=0, y′(0)=5.
Enter an exact answer. Enclose arguments of functions in parentheses. For example, sin(2x).

y(t) = _____

2. Use the method of variation of parameters to find a particular solution of the differential equation

y′′−2y′−15y=384e^−t.

Y(t) = ______

1. Use the method of reduction of order to find a second solution of the differential equation
t^2 y double prime + 10t y prime - 10y = 0, t > 0 given the solution y1 = t

A. y2 = t^-1
B. y2 = 1
C.y2 = t
D.y2 = t^-10
E.y2 = t^10
F y2 = t^11
G. y2 = t^-11

Solve the initial value problem
y
iv + 2y
000
+ 11y
00
+ 18y
0 + 18 = 0, y(0) = 2, y
0
(0) = 3, y
00(0) = −11, y
000(0) = −23

solve f(x, u_x,u_z)=g(y,u_y,u_z) by Jacobi method.

Solve (x+y)(p+q) =z-1

Solve (b-c/a)yzp+(c-a/b)xzq=(a-b/c)xy.

Solve- (3x+y-z)p + (x+y+z)q = 2(z+y)

Find the solution of the initial-value problem and determine its interval of existence (i.e domain of the resulting function y). (i) dy dt = 1+t2 t , y(t = 1) = 0. (ii) (t + 1)dy dt = 1−y, y(t = 0) = 3. [Hint: Let A = −(±e−C).]