The solution of differential equation dy/dx + (y+3x)/loge(y+3x) + 3 = 0 is:
(where C is a constant of integration.)
The solution of differential equation dy/dx + (y+3x)/loge(y+3x) + 3 = 0 is:
(where C is a constant of integration.)
Option 1 -
y + 3x - 1/2(logₑ x)² = c
Option 2 -
x - 1/2(logₑ(y + 3x))² = C
Option 3 -
x - 1/2logₑ(y + 3x) = C
Option 4 -
x - logₑ(y + 3x) = C
Asked by Shiksha User
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1 Answer
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Correct Option - 2
Detailed Solution:dy/dx = (y-3x)/ln (y-3x) - 3
dy/dx + 3 = (y+3x)/ln (y+3x)
d/dx (y+3x) = (y+3x)/ln (y+3x)
∫ (ln (y+3x)/ (y+3x) d (y+3x) = ∫ dx
Let ln (y+3x) = t
1/ (y+3x) d (y+3x) = dt
∫ tdt = ∫ dx
t²/2 = x+c
(ln (y+3x)²/2 = x+c
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