For Problems 7–21, verify that the given function is a solution to the given differential equation ( c 1 and c 2 are arbitrary constants), and state the maximum interval over which the solution is valid. y ( x ) = c 1 x 1 / 2 , y ′ = y 2 x .
For Problems 7–21, verify that the given function is a solution to the given differential equation ( c 1 and c 2 are arbitrary constants), and state the maximum interval over which the solution is valid. y ( x ) = c 1 x 1 / 2 , y ′ = y 2 x .
Solution Summary: The author explains how to determine whether y(x)=c_1x 1/2 is the solution of the differential equation.
For Problems 7–21, verify that the given function is a solution to the given differential equation (
c
1
and
c
2
are arbitrary constants), and state the maximum interval over which the solution is valid.
y
(
x
)
=
c
1
x
1
/
2
,
y
′
=
y
2
x
.
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.
The instructions say:
For each differential equation in Problems 1–21, find the general solution by finding the homogeneous solution and a particular solution.
The first image below is the problem, the second is the answer. I'm able to get the homogeneous solution but am struggling with getting the particular solution to get to the answer the textbook provides.
For each dif erential equation in Problems 1–21, find the general solutionby finding the homogeneous solution and a particular solution.
Please DO NOT YOU THE PI method where 1/f(r) * x. Dont do that.
Instead do this, assume for yp = to something, do the 1 and 2 derivative of it and then plug it in the equation to find the answer.
Are the functions f, g, and h given below linearly independent?
f(x) = e2" + cos(7x), g(æ)= e2 – cos(7x), h(x) = cos(7x).
If they are independent, enter all zeroes. If they are not linearly independent, find a nontrivial solution to the equation below. Be sure you can justify your answer.
(e2z + cos(7x)) +
(e2z – cos(7x)) +
(cos(7x)) = 0. help (numbers)
Chapter 1 Solutions
Differential Equations and Linear Algebra (4th Edition)
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