So there's this question I've to do. I got through until a certain point and now I'm stuck. >->
1&2The question:
The rate of deterioration of a product in a container is proportional to the amount of product present. At time t, the amount of product is x.
(i) State the diffrential equation...
I got the following two integral for the a particular solution of a 2nd order linear ODE $$(D-a)(D-b)y = g(x)$$
by using inverse operators ##\frac{1}{D-a}## and ##\frac{1}{D-b}##. The two different integrals are obtained by operating these operators in different order on y to get a particular...
Homework Statement
Find the values of the constant a for which the problem y''(t)+ay(t)=y(t+π), t∈ℝ, has a solution with period 2π
which is not identically zero. Also determine all such solutions
Homework Equations
With help of Fourier series I know that :
Cn(y''(t))= -n2*Cn(y(t))
Cn(y(t+π)) =...
I am given a modified SIR model in which the rate of decrease of susceptibles S is proportional to the number of susceptibles and the square-root of the number if infectives, I. If the number R of those who have been removed or recovered increases in proportion to the infectives, we have the...
Homework Statement
I Have a differential equation y'' -xy'-y=0 and I must solve it by means of a power series and find the general term. I actually solved the most of it but I have problem to decide it in term of a ∑ notation!
Homework Equations
y'' -xy'-y=0
The Attempt at a Solution
I know...
1. I need to find a condition that the equation will have a integration factor from the shape K(x*y).
(K-integration factor sign)
2.the eq from the shape M(x,y)dx+N(x,y)dy=0 ,not have to be exact!3. i tried to open from the basics. d(k(x*y)M(x,y))/dy=d((k(x*y)N(x,y))/dx.
and i used the fact...
Homework Statement
There are now about 3300 different human "language families" in the whole world. Assume that all these are derived from a single original language, and that a language family develops into 1.58 language families every 5860 years. About how long ago was the single original...
Homework Statement
r''-(theta')^2=-g reads: second derivative of r minus the first derivative of theta squared equals negative g
2(r')theta'+(r)theta''=0 reads: 2 times the first derivative of r times the first derivative of theta plus r times the second derivative of theta.
both r and...
Homework Statement
let x + y = u and y = uv
Expand dx and dy in terms of du and dv
Homework Equations
The Attempt at a Solution
i got this answer:
dy = udv + vdu
and
dx = du - udv - vdu
is this correct?