Verifying general solutions Verify that the given function is a solution of the differential equation that follows it. 44. u ( t ) = C e 1 / ( 4 t 4 ) ; u ′ ( t ) + 1 t 5 u ( t ) = 0
Verifying general solutions Verify that the given function is a solution of the differential equation that follows it. 44. u ( t ) = C e 1 / ( 4 t 4 ) ; u ′ ( t ) + 1 t 5 u ( t ) = 0
Solution Summary: The author explains how to verify the function u(t)=Ce1 (4t
Verifying general solutionsVerify that the given function is a solution of the differential equation that follows it.
44.
u
(
t
)
=
C
e
1
/
(
4
t
4
)
;
u
′
(
t
)
+
1
t
5
u
(
t
)
=
0
With integration, one of the major concepts of calculus. Differentiation is the derivative or rate of change of a function with respect to the independent variable.
Suppose that a parachutist with linear drag (m=50 kg, c=12.5kg/s) jumps from an airplane flying at an altitude of a kilometer with a horizontal velocity of 220 m/s relative to the ground.
a) Write a system of four differential equations for x,y,vx=dx/dt and vy=dy/dt.
b) If theinitial horizontal position is defined as x=0, use Euler’s methods with t=0.4 s to compute the jumper’s position over the first 40 s.
c) Develop plots of y versus t and y versus x. Use the plot to graphically estimate when and where the jumper would hit the ground if the chute failed to open.
A 200 gallon tank initially contains 100 gallons of water with 20 pounds of salt. A salt solution with 1/5
pound of salt per gallon is added to the tank at 10 gal/min, and the resulting mixture is drained out at 5
gal/min. Let Q(t) denote the quantity (lbs) of salt at time t (min).
(a) Write a differential equation for Q(t) which is valid up until the point at which the tank overflows.
Q' (t) =
=
(b) Find the quantity of salt in the tank as it's about to overflow.
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Find the derivative of the function.
F(x) = -1/12/2
x2
f'(x) =
Need a deep-dive on the concept behind this application? Look no further. Learn more about this topic, computer-science and related others by exploring similar questions and additional content below.
01 - What Is A Differential Equation in Calculus? Learn to Solve Ordinary Differential Equations.; Author: Math and Science;https://www.youtube.com/watch?v=K80YEHQpx9g;License: Standard YouTube License, CC-BY
Higher Order Differential Equation with constant coefficient (GATE) (Part 1) l GATE 2018; Author: GATE Lectures by Dishank;https://www.youtube.com/watch?v=ODxP7BbqAjA;License: Standard YouTube License, CC-BY