Learn more about our help with Assignments: Differential Equations
Search & Filtering
Differential Equations
A bowl of water has a temperature of 50◦C. It is put into a refrigerator where the temperature is 5◦C. After 0.5 hours, the water is stirred and its temperature is measured to be 20◦C. It is then left to cool further, take t in Newton’s law of cooling to be measured in
minutes. Use Newton’s law of cooling to predict when the temperature will be 10◦C.
minutes. Use Newton’s law of cooling to predict when the temperature will be 10◦C.
Differential Equations
solve y'=x+y by power series method of solution
Differential Equations
A skydiver weighing 174 lbf (including equipment) falls vertically downward from an altitude of 4000 ft and opens the parachute after 10s of free fall. Assume that the force of air resistance, which is directed opposite to the velocity, is 0.76 |v| when the parachute is closed and 12|v| when the parachute is open, where the velocity v is measured in ft/s.
Measure the positive direction of motion downward. Consider that x(0) = 0 ft. Use g = 32 ft/s^2. Round your answers to two decimal places.
(a) Find the speed of the skydiver when the parachute opens. (the tolerance is +/- 2 percent)
v(10) = _______ ft/s
(b) Find the distance fallen before the parachute opens.(the tolerance is +/- 2 percent)
x(10) = _________ft
(c) What is the limiting velocity vl after the parachute opens?(the tolerance is +/- 2 percent)
vl = _____ ft/s
Measure the positive direction of motion downward. Consider that x(0) = 0 ft. Use g = 32 ft/s^2. Round your answers to two decimal places.
(a) Find the speed of the skydiver when the parachute opens. (the tolerance is +/- 2 percent)
v(10) = _______ ft/s
(b) Find the distance fallen before the parachute opens.(the tolerance is +/- 2 percent)
x(10) = _________ft
(c) What is the limiting velocity vl after the parachute opens?(the tolerance is +/- 2 percent)
vl = _____ ft/s
Differential Equations
Express sin inverse x in the form of a power series summation an x^n by solving y'= (1-x^2) ^(1/2) in two ways use this result to obtain the formula pi/6=1/2+ 1/2 .1/(3.(2)^3)+1/2.3/4.1/5.(2)^5)+ etc ......
Differential Equations
solve y'+y= 1 by power series solution method
Differential Equations
What is the standard form of homogeneous differential equation of order n.
Differential Equations
Write the Integrating factor of the Differential Equation dy/dx
+ x/1+x *
y=ex
+ x/1+x *
y=ex
Differential Equations
Solve the differential equation by variation of parameters.
4y'' − 8y' + 8y = e^x sec x
y(x) =______
4y'' − 8y' + 8y = e^x sec x
y(x) =______
Differential Equations
Consider how the methods of undetermined coefficients and variation of parameters can be combined to solve the given differential equation. Carry out your ideas to solve the differential equation.
y'' − 2y' + y = 4x^2 − 1 + x^−1e^x
y(x) =____
y'' − 2y' + y = 4x^2 − 1 + x^−1e^x
y(x) =____
Differential Equations
Solve the differential equation by variation of parameters.
y'' + 3y' + 2y = 1/ 1 + e^x
y(x) =____
y'' + 3y' + 2y = 1/ 1 + e^x
y(x) =____
