FIND THE GENERAL SOLUTION TO THE DE: Y”’ + 4Y” – Y’ –
4Y = 0
COMPUTE:
L {7 e 3t – 5 cos ( 2t ) – 4 t 2
}
COMPUTE:
L – 1 {(3s + 6 ) / [ s ( s 2 + s – 6 ) ]
}
SOLVE THE INITIAL VALUE PROBLEM USING LAPLACE
TRANSFORMS:
Y” + 6Y’ + 5Y = 12 e t
WHEN : f ( 0 ) = -...
A) Solve the initial value problem:
8x−4y√(x^2+1) * dy/dx=0
y(0)=−8
y(x)=
B) Find the function y=y(x) (for x>0 ) which
satisfies the separable differential equation
dy/dx=(10+16x)/xy^2 ; x>0
with the initial condition y(1)=2
y=
C) Find the solution to the differential equation
dy/dt=0.2(y−150)
if y=30 when t=0
y=
Power series
Find the particular solution of the differential equation:
(x^2+1)y"+xy'-4y=0 given the boundary conditions x=0, y=1 and y'=1.
Use only the 7th degree term of the solution. Solve for y at x=2.
Write your answer in whole number.
1. The differential equation y''+4y=f(t) and
y'(0)=y(0)=0
a. Find the transfer function and impulse response.
b. If f(t)=u(t)-u(t-1). Find the y(t) by convolution and Laplace
techniques. u(t) is unit step function.
c. If f(t)= cos(t) ; find the y(t) by convolution and Laplace
techniques.
2. The differential equation y''+3y'+2y=e^(-3t) and
y'(0)=y(0)=0
a. Find the system transfer function and impulse response.
b. Find the y(t) by convolution and Laplace techniques.
3. y''+3y'+2y=f(t) and
y'(0)=y(0)=0
Plot y(t) without any calculations and write...