olve the following linear inhomogeneous equations using integrating factors. For each question you need to enter: The function u(x) The function v(x), including the integrating constant C The general solution y(x) without the given condition applied The general solution after applying the given condition y' - 2y = xe* with y(0) = 1 (x) = e -2x 2x (x) = -xe* e²x dx + C (x) = -xẻ -ẽ +C-e
olve the following linear inhomogeneous equations using integrating factors. For each question you need to enter: The function u(x) The function v(x), including the integrating constant C The general solution y(x) without the given condition applied The general solution after applying the given condition y' - 2y = xe* with y(0) = 1 (x) = e -2x 2x (x) = -xe* e²x dx + C (x) = -xẻ -ẽ +C-e
Calculus For The Life Sciences
2nd Edition
ISBN:9780321964038
Author:GREENWELL, Raymond N., RITCHEY, Nathan P., Lial, Margaret L.
Publisher:GREENWELL, Raymond N., RITCHEY, Nathan P., Lial, Margaret L.
Chapter11: Differential Equations
Section11.1: Solutions Of Elementary And Separable Differential Equations
Problem 54E: Plant Growth Researchers have found that the probability P that a plant will grow to radius R can be...
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![Solve the following linear inhomogeneous equations using integrating factors. For each question you need to enter:
The function u(x)
The function v(x), including the integrating constant C
The general solution y(x) without the given condition applied
The general solution after applying the given condition
a. y' - 2y = xe* with y(0) = 1
u (x) =
v (x) = -xe* - e²x dx + C
y (x) = -xet - et +C-e²x
-2x
y (x) = -xet - et + 2e²x
b. y' + 2xy = x3 with y(0) = 1
U (x) =
v (x) =
y (x) =
X
(x² − 1) + C² e ²¹²
3
y (x) = 1/²(x²-1) + 2²/e-x²](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fb8e0ad34-47bd-4edd-8e64-7fbb4be3cef6%2Ff9428835-86d3-43ec-a2f2-2c1349d3b4e3%2Fx786g3f_processed.png&w=3840&q=75)
Transcribed Image Text:Solve the following linear inhomogeneous equations using integrating factors. For each question you need to enter:
The function u(x)
The function v(x), including the integrating constant C
The general solution y(x) without the given condition applied
The general solution after applying the given condition
a. y' - 2y = xe* with y(0) = 1
u (x) =
v (x) = -xe* - e²x dx + C
y (x) = -xet - et +C-e²x
-2x
y (x) = -xet - et + 2e²x
b. y' + 2xy = x3 with y(0) = 1
U (x) =
v (x) =
y (x) =
X
(x² − 1) + C² e ²¹²
3
y (x) = 1/²(x²-1) + 2²/e-x²
![c. xy' = x cos x - 2 sin x - 2y with y(π) = 0
U (x) =
v (x) =
y (x) = sin(x) +
y (x) = sin(x) +
u (x) =
d. xy' = 2x² + y with y(1) = 2
v (x) =
-1
y (x) = x³ + C-x
4 cos(x)
y (x) = x² + x
x³+x
4 cos(x)
4 sin(x)
4 sin(x)
x²
بان](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fb8e0ad34-47bd-4edd-8e64-7fbb4be3cef6%2Ff9428835-86d3-43ec-a2f2-2c1349d3b4e3%2Fjigyjng_processed.png&w=3840&q=75)
Transcribed Image Text:c. xy' = x cos x - 2 sin x - 2y with y(π) = 0
U (x) =
v (x) =
y (x) = sin(x) +
y (x) = sin(x) +
u (x) =
d. xy' = 2x² + y with y(1) = 2
v (x) =
-1
y (x) = x³ + C-x
4 cos(x)
y (x) = x² + x
x³+x
4 cos(x)
4 sin(x)
4 sin(x)
x²
بان
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