Verifying general solutions Verify that the given function is a solution of the differential equation that follows it. 49. z ( t ) = C 1 e − t + C 2 e 2 t + C 3 e − 3 t − e t ; z ‴ ( t ) + 2 z ″ ( t ) − 5 z ′ ( t ) − 6 z ( t ) = 8 e t
Verifying general solutions Verify that the given function is a solution of the differential equation that follows it. 49. z ( t ) = C 1 e − t + C 2 e 2 t + C 3 e − 3 t − e t ; z ‴ ( t ) + 2 z ″ ( t ) − 5 z ′ ( t ) − 6 z ( t ) = 8 e t
Solution Summary: The author explains that the first derivative of z(t)=C_1e-t+
Verifying general solutionsVerify that the given function is a solution of the differential equation that follows it.
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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.
find the general solution to the following differential equation by using VARIATION OF PARAMETER method.
y''+4y'+5y=e-2xsecx
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) =
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(b) Find the quantity of salt in the tank as it's about to overflow.
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Find A PARTICULAR solution of the following differential equation by using UNDE-TERMINED COEFFICIENTS METHOD.
y” + 3y’ + 2y = ex sin x
Need a deep-dive on the concept behind this application? Look no further. Learn more about this topic, calculus 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