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1. Solve the given differential equation, subject to the initial conditions:
. x2y''-3xy'+4y = 0
. y(1) = 5, y'(1) = 3
2. Find two linearly independent power series solutions for each differential equation about the ordinary point x=0
Y'' - xy' - (x+2)y=o
3. Use the definition of the Laplace Transform, to find
L{e-t cosht}
4. Find f(t) if : f(t)=L-1
5. Solve : y'+y= f(t)
where: f(t) = { 1 if 0 ≤ t < 1
{-1 if t ≥ 1
Recall that if f(t) = { g(t) if 0 ≤ t < a
{ h(t) if t ≥ 1
Then f(t)=g(t)-g(t)u(t-a)+h(t)u(t-a)
6. y'(t) = cos t+
solve for x and y 2x+3y=12 and 30x+11y=112
Here we know x can only be 1 or -1. so if it is 1 ans is 2. if x is -1, for n even ans will be 2 if x is -1 and n is odd ans will ne -2. so we can see evenfor negative x also an
integrate sin(x) dx
log base 5 (3-2x) + log base 5 (2+x) = 1
Observe that natural numbers do not have a zero. This shortcoming is made good when we consider the set of whole numbers. The set of whole numbe
assignment for appications of derivatives
There are 20 defective bulbs in a box of 100 bulbs.if 10bulbs are choosen at random then what is the probability of there are just 3defective bulbs
Difference Between Experiment and Outcome Experiment is an operation that produces outcomes which can be observed. Outcome/Event is the result of an experiment.
The area of a parallelogram is x 8 . If the base is x 4 , what is the height in terms of x? Since the area of a parallelogram is A = base times height, then the area divided by
alternate segment theorum
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