Find a general solution for y in terms of x that satisfies the first-order linear differential equation. xy' = y − 2x, x > 0 Recall the standard form of a first-order linear differential equation is given by y' + P(x)y = Q(x), for some functions P(x), Q(x). Write the given differential equation xy' = y − 2x in standard form. Assume x ≠ 0 so that we may divide by x. Also assume x > 0 so |x| = x and we will not require any absolute value signs. y' + ( )y = -2 Identify the functions P(x) and Q(x) from the standard form of the first-order linear differential equation. P(x) = Q(x) =
Find a general solution for y in terms of x that satisfies the first-order linear differential equation. xy' = y − 2x, x > 0 Recall the standard form of a first-order linear differential equation is given by y' + P(x)y = Q(x), for some functions P(x), Q(x). Write the given differential equation xy' = y − 2x in standard form. Assume x ≠ 0 so that we may divide by x. Also assume x > 0 so |x| = x and we will not require any absolute value signs. y' + ( )y = -2 Identify the functions P(x) and Q(x) from the standard form of the first-order linear differential equation. P(x) = Q(x) =
Find a general solution for y in terms of x that satisfies the first-order linear differential equation. xy' = y − 2x, x > 0 Recall the standard form of a first-order linear differential equation is given by y' + P(x)y = Q(x), for some functions P(x), Q(x). Write the given differential equation xy' = y − 2x in standard form. Assume x ≠ 0 so that we may divide by x. Also assume x > 0 so |x| = x and we will not require any absolute value signs. y' + ( )y = -2 Identify the functions P(x) and Q(x) from the standard form of the first-order linear differential equation. P(x) = Q(x) =
Find a general solution for y in terms of x that satisfies the first-order linear differential equation.
xy' = y − 2x, x > 0
Recall the standard form of a first-order linear differential equation is given by
y' + P(x)y = Q(x),
for some functions
P(x), Q(x).
Write the given differential equation
xy' = y − 2x
in standard form. Assume
x ≠ 0
so that we may divide by x. Also assume x > 0 so |x| = x and we will not require any absolute value signs.
y' + ( )y = -2
Identify the functions
P(x) and Q(x)
from the standard form of the first-order linear differential equation.
P(x)
=
Q(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.
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