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The differential equation 4yy’ - 12x = 0, satisfying condition y (1) = 3. Then the point (5, 3) will lie:
  • a)
    on the solution curve
  • b)
    outside the solution curve
  • c)
    Inside the solution curve
  • d)
    can-not say
Correct answer is option 'C'. Can you explain this answer?
Verified Answer
The differential equation 4yy’ - 12x = 0, satisfying condition y...
Since given differential equation is
4yy’ - 12x = 0
4y dy = + 12x dx
On integrating both the sides
2y2 = 6x2 + c
2y2 - 6x2 = c
Given y (1) = 3
Thus, 2(3)2 - 6(1)2 = c
18 - 6 = C
C = 12
Thus, 2y2 - 6x= 12
Now, f (x, y) = 2y2 - 6x2 - 12
At point (5, 3)
= 50 - 54 - 12
= -16
Thus, the point will lie inside the solution curve.
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The differential equation 4yy’ - 12x = 0, satisfying condition y (1) = 3. Then the point (5, 3) will lie:a)on the solution curveb)outside the solution curvec)Inside the solution curved)can-not sayCorrect answer is option 'C'. Can you explain this answer?
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