Differential Equations Answers

Gerry is to memorize 150 terms for a quiz. If the rate by which the number of terms Gerry memorizes is directly proportional to the number of terms already memorized and the number of remaining terms; and that initially Gerry knows 5 terms and 20 terms 5 minutes later. At what time is he half done?

Gerry is to memorize 150 terms for a quiz. If the rate by which the number of terms Gerry memorizes is directly proportional to the number of terms already memorized and the number of remaining terms; and that initially Gerry knows 5 terms and 20 terms 5 minutes later. At what time is he half done?

The position vector of a particle P of mass 6kg at time t seconds is r where r=[(18t-4t^3)I+ t^2j]m determine to 2 decimal places the value of t for which the velocity and the acceleration vectors of P are at right angles

Solve by I.F method

-2xydy+(x²+y²)dx = 0

Solve (3y + 2x + 4) * d * x - (4x + 6y + 5) * d * y = 0

The only integral surface of the equation and 2q (z - px- qy) 1+ q^2 which is circumscribed about paraboloid 2x= y^2 + z^2 and which touches it along its section by the plane y + 1 = 0 is = ?

the characteristic of the equation PQ=x and the integral surface which passes through the curve y=1/2 z=x are =?

1. Using the Frobenius method solve the following ODE:

x²y" + 4xy' + (x² + 2)y = 0

2. Determine the first and second order partial derivatives for the function:

u(x,t) = Ce^(1-n²π²)tsin(nπx)

3. Obtain the Fourier series for the following function:

0 -π < x < 0

f(x) =

sin x 0 < x < π