Diffrential equations Definition and 11 Threads

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...

How would I take the laplace transform of f(t)= te^tsin^2(t)?

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?

solve the diffrential equation: xy' = x(e^(-y/x)) + y answer: y = xln|lncx| problem: i don't get it can anyone explain