Let y = y(x) be the solution of the differential equation (x - x³) dy = (y + yx² – 3x⁴ )dx, x > 2. If y(3) = 3 then y(4) is equal to
Let y = y(x) be the solution of the differential equation (x - x³) dy = (y + yx² – 3x⁴ )dx, x > 2. If y(3) = 3 then y(4) is equal to
Option 1 -
12
Option 2 -
4
Option 3 -
8
Option 4 -
16
Asked by Shiksha User
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1 Answer
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Correct Option - 1
Detailed Solution:. xdy - ydx - x² (xdy + ydx) + 3x? dx = 0
⇒ (xdy - ydx)/x² - (xdy + ydx) + 3x²dx = 0 ⇒ d (y/x) - d (xy) + d (x³) = 0
Integrate both side, we get
y/x - xy + x³ = c
Put x = 3, y = 3
⇒ 1 - 9 + 27 = c
c = 19
Put x = 4
y/4 - 4y = 19 - 64
⇒ y = 12
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