a)Find the equation of the solution through the point (x,y)=(0,−7). Your answer should be of the form x=f(y) or y=f(x), whichever is appropriate.
b)Find the equation of the solution through the point (x,y)=(7,0). Your answer should be of the form x=f(y) or y=f(x), whichever is appropriate.
Help!
Solve the differential equation dy/dx=x/(36y).?
2015-01-19 12:37 am
回答 (2)
2015-01-19 9:44 am
✔ 最佳答案
a)dy/dx = x/(36y)
separate variables
36y dy = x dx
∫36y dy = ∫x dx
18y² = ½x² + C
(0, -7)
18*(-7)² = ½*0² + C
C = 882
18y² = ½x² + 882
36y² = x² + 1764
y² = 1/36 ( x² + 1764 )
possible solutions
y = ±⅙√(x² + 1764)
but the term √(x² + 1764) > 0, i.e to get (0, -7) in the term ±⅙ use -⅙
solution:
```````````````` y = -⅙√(x² + 1764)
b)
18y² = ½x² + C
18*0² = ½*7² + C
C = -49/2
18y² = ½x² - 49/2
36y² = x² - 49
y² = 1/36 (x² - 49)
y = ±⅙( x² - 49 )
solutions:
y = -⅙( x² - 49 ) and y = ⅙( x² - 49 )
2015-01-19 12:46 am
dy/dx = x/36y
dy = (x/36y) dx
36 y dy = x dx
-Integrate both sides
18y^2 = 0.5x^2 (+ c.)
36y^2 = x^2 + c
0 + c = 1764
36y^2 = x^2 + 1764
y^2 = (x^2 / 36) + 49
y = sqrt( x^2 / 36 + 49)
b. 0 = 49 + c
y^2 = (x^2 / 36) + (49/36).
The equation in all circumstances is y = sqrt( x^2/36 + c)
c is 49 in part a, and 49/36 in part b.
dy = (x/36y) dx
36 y dy = x dx
-Integrate both sides
18y^2 = 0.5x^2 (+ c.)
36y^2 = x^2 + c
0 + c = 1764
36y^2 = x^2 + 1764
y^2 = (x^2 / 36) + 49
y = sqrt( x^2 / 36 + 49)
b. 0 = 49 + c
y^2 = (x^2 / 36) + (49/36).
The equation in all circumstances is y = sqrt( x^2/36 + c)
c is 49 in part a, and 49/36 in part b.
收錄日期: 2021-04-15 18:00:17
原文連結 [永久失效]:
https://hk.answers.yahoo.com/question/index?qid=20150118163727AA0rGVz