Use reduction of order to find a second solution to a differential equation.

Given that y1(x)=e^-x is a solution of y'' + 2y' + y =0, find second solution using the method of reduction of order. I substituted y =ve^-x so y' = v'e^-x - v^-x; y''= v''e^-x -v'e^-x +v e^-x I came out of that with v''e^-x + v'e^-x =0 I think the next step is to seperate variables. Looking for help to finish the pro ...continues

Solving Ordinary Differential Equation using Laplace Transform

(1) Use Laplace Transforms to solve Differential Equation y'' - 8y' + 20 y = t (e^t) , given that y(0) = 0 , y'(0) = 0 (2) Use Laplace Transforms to solve Differential Equation y''' + 2y'' - y' - 2y = Sin 3t , given that y(0)=0 , y'(0)=0 ,y''(0)=0, y'''(0)=1 Note: To see the questions in their mathematic ...continues

Nonhomogeneous Differential Equations : Method of Undetermined Coefficients

Using the method of undetermined coefficients to find the particular solution of the nonhomogeneous equation, find the solution of the following d.e. satisfying the given initial conditions y"+4y=x^2+3e^x y(0)=0 y'(0)=2

A scientist prepares a sample of radioactive substance.

A scientist prepares a sample of radioactive substance. One year later, the sample contains 3 grams of the substance; 2 year later there is only 1 gram. Determine how much of the radioactive substance was present initially. Use words to describe the solution steps. (not just symbols) Please Attach the solution as a separa ...continues

Applications of Derivatives and Differential Equations

8. a. Let y(t) be the amount of a radiactive material with relative decay rate k. Let Q(t) be the decay rate. Use the differential equation for y (not the solution formula) to show that the quantity Q also undergoes exponential decay with rate constant k. b. It is sometimes easier to measure the rate of radioactive decay t ...continues

Strontium 90 is a radioactive isotope produced in hydrogen bomb explosions.

Strontium 90 is a radioactive isotope produced in hydrogen bomb explosions. The aboveground nuclear test ban treaty of 1963 was based on evidence of Sr-90 contamination of milk and human bones. The half-life of Sr-90 is 29 years. Suppose no new sources of Sr-90 have contaminated the atmosphere since 1963. Determine what frac ...continues

Applications of Derivatives and Differential Equations

The relative decay rate of naturally occurring uranium U-238 was given in Example 4. Scientists estimate the age of the earth to be about 4.55 billion yr. Determine the fraction of the U-238 present when the earth was formed that is still present as U-238. EXAMPLE 4: A 1-G sample of pure uranium produces about 740,000 de ...continues

Differential Equations : Variation of Parameters

Determine the particular solution for the following nonhomogeneous differential equation using the method of variation of parameters Y” + y =tan(x); 0< x < pi/2 I got characteristic equation as y = U1 sin(x) + U2 cos (x) I was able to get thru to set the original D.E. to u’1 (x) cos (x) - u’2 (x) sin (x) = tan (x) ...continues

First order differential equations-mixing problem

Consider two tanks, labeled Tank A and Tank B. Tank A contains 100 gallons of solution in which is dissolved 20 lbs of salt. Tank B contains 200 gallons of solution in which is dissolved 40 lbs of salt. Pure water flows into tank A at a rate of 5 gal/s. There is a drain at the bottom of tank A. The solution leaves tank A via thi ...continues

what is the probability that among the 12 months of the year there are 3 non necessarily consecutive months containing exactly 4 birthdays?

Given 20 people, what is the probability that among the 12 months of the year there are 3 non necessarily consecutive months containing exactly 4 birthdays? hints: 1. to count the number of elements of the state space, look at the following proposition: There are ( n + r -1 choose r-1 ) distinct nonnegative integer valu ...continues