JEE Exam > JEE Questions > Which equation has the solution, y = 4sin3x?a...
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Which equation has the solution, y = 4sin3x?
- a)(dy/dx)+8y=0
- b)(dy/dx)-8y=0
- c)(d2y/dx2)+9y=0
- d)(d2y/dx2)-9y=0
Correct answer is option 'C'. Can you explain this answer?
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Most Upvoted Answer
Which equation has the solution, y = 4sin3x?a)(dy/dx)+8y=0b)(dy/dx)-8y...
Explanation:
Given Solution:
y = 4sin3x
First Derivative:
To find the first derivative of y, we differentiate with respect to x:
dy/dx = 4(3)cos3x = 12cos3x
Second Derivative:
To find the second derivative of y, we differentiate dy/dx with respect to x:
d^2y/dx^2 = -12(3)sin3x = -36sin3x
Substitute into the Differential Equation Options:
a) (dy/dx) + 8y = 12cos3x + 32sin3x ≠ 0
b) (dy/dx) - 8y = 12cos3x - 32sin3x ≠ 0
c) (d^2y/dx^2) + 9y = -36sin3x + 36sin3x = 0
d) (d^2y/dx^2) - 9y = -36sin3x - 36sin3x ≠ 0
Conclusion:
The equation that has the solution y = 4sin3x is option C, which is (d^2y/dx^2) + 9y = 0. This option satisfies the given solution and the differential equation.
Given Solution:
y = 4sin3x
First Derivative:
To find the first derivative of y, we differentiate with respect to x:
dy/dx = 4(3)cos3x = 12cos3x
Second Derivative:
To find the second derivative of y, we differentiate dy/dx with respect to x:
d^2y/dx^2 = -12(3)sin3x = -36sin3x
Substitute into the Differential Equation Options:
a) (dy/dx) + 8y = 12cos3x + 32sin3x ≠ 0
b) (dy/dx) - 8y = 12cos3x - 32sin3x ≠ 0
c) (d^2y/dx^2) + 9y = -36sin3x + 36sin3x = 0
d) (d^2y/dx^2) - 9y = -36sin3x - 36sin3x ≠ 0
Conclusion:
The equation that has the solution y = 4sin3x is option C, which is (d^2y/dx^2) + 9y = 0. This option satisfies the given solution and the differential equation.
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Which equation has the solution, y = 4sin3x?a)(dy/dx)+8y=0b)(dy/dx)-8y=0c)(d2y/dx2)+9y=0d)(d2y/dx2)-9y=0Correct answer is option 'C'. Can you explain this answer?
Question Description
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