Method of variation of parameters
Use the method of variation of parameters to determine a general solution to differential equation: ty''+(1-2t)y'+(t-1)y=te^t given that y1=e^t and y2=e^t (ln t) are two linearly independent solutions to the corresponding homogenous equation.
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Solve the given differential equation by using the substitution u=y' (Use C1 and C2as arbitrary constants. Use x as the independent variable.)
Find a linear differential operator that annihilates the given function. (Use D for the differential operator.)
Suggest: f : R----> R is continuous, a, b are functions from R to R and are differentiable on R. g(x) = integral of f(t)dt with upper limit = b(x) and lower limit = a(x) the problem is to determine a general formula for the derivative of g at x
Prove the validity of the limit lim x->x_0 (ax+b)=ax_0+b by converting to a statement about sequences.
How can you find the number of possible outcomes of a playoff between two teams where the first team to win four games wins the playoff?
Determine the general solution of given differential equation. Provide largest interval over which the general solution is defined. Find out transient term.
Use reduction of order or formula to find a second solution
The radioactive isotope of lead, Pb-209, decays at the rate proportional to the amount present at time t and has a half-life of 3.3 hours. If 1 gram of this isotope is present initially, how long will it take for 95% of the lead to decay?
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