2. Find the explicit solution to the following initial value conditions: • (1 + x²)dy + x(1+4y²)dx = 0, y(1) = 0 dy dx dy = y² x²-1' y(2)=2 Xx +y=4x+1, y(1) = 8 dr ⚫ y' + tan xy = cos² x, y(0) = -1 (ex + y)dx+(2+x+ ye³)dy = 0, y(0) = 1 xy2 dy = y³-x³, y(1) = 2 dx ²-4-5y=0, y(1) = 0, y′(1) = 2 dt 4y" - y = xe/2, y(0) = 1, y'(0) = 0
2. Find the explicit solution to the following initial value conditions: • (1 + x²)dy + x(1+4y²)dx = 0, y(1) = 0 dy dx dy = y² x²-1' y(2)=2 Xx +y=4x+1, y(1) = 8 dr ⚫ y' + tan xy = cos² x, y(0) = -1 (ex + y)dx+(2+x+ ye³)dy = 0, y(0) = 1 xy2 dy = y³-x³, y(1) = 2 dx ²-4-5y=0, y(1) = 0, y′(1) = 2 dt 4y" - y = xe/2, y(0) = 1, y'(0) = 0
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.
Chapter6: Applications Of The Derivative
Section6.CR: Chapter 6 Review
Problem 36CR
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Solve the following question by hand and without the use of AI. My goal is to learn how to perform the mathematical calulcations. Thank you!
![2. Find the explicit solution to the following initial value conditions:
• (1 + x²)dy + x(1+4y²)dx = 0, y(1) = 0
dy
dx
dy
=
y²
x²-1'
y(2)=2
Xx +y=4x+1, y(1) = 8
dr
⚫ y' + tan xy = cos² x, y(0) = -1
(ex + y)dx+(2+x+ ye³)dy = 0, y(0) = 1
xy2 dy = y³-x³, y(1) = 2
dx
²-4-5y=0, y(1) = 0, y′(1) = 2
dt
4y" - y = xe/2, y(0) = 1, y'(0) = 0](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F9669f5d5-395e-4f01-8d20-5c42ebd987c5%2Fe65a1e8a-8f6a-44f0-9742-648e34634b1f%2Fwp3x8s_processed.png&w=3840&q=75)
Transcribed Image Text:2. Find the explicit solution to the following initial value conditions:
• (1 + x²)dy + x(1+4y²)dx = 0, y(1) = 0
dy
dx
dy
=
y²
x²-1'
y(2)=2
Xx +y=4x+1, y(1) = 8
dr
⚫ y' + tan xy = cos² x, y(0) = -1
(ex + y)dx+(2+x+ ye³)dy = 0, y(0) = 1
xy2 dy = y³-x³, y(1) = 2
dx
²-4-5y=0, y(1) = 0, y′(1) = 2
dt
4y" - y = xe/2, y(0) = 1, y'(0) = 0
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