Question:
The order of the differential equation obtained by eliminating arbitrary constants in the family of curves c1y = (c2 + c3)ex+c4 is
The order of the differential equation obtained by eliminating arbitrary constants in the family of curves c1y = (c2 + c3)ex+c4 is
Updated On: Apr 2, 2025
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The Correct Option is A
Solution and Explanation
The solution to the differential equation is given by: \[ y = \left[ \left( \frac{C_2 + C_3}{C_1} \right) e^{C_4} \right] e^x = A e^x, \] where \( A = \left( \frac{C_2 + C_3}{C_1} \right) e^{C_4} \) is a consolidated constant.
The order of the differential equation is determined by the number of independent arbitrary constants, which in this case is 1.
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