The number of arbitrary constants that appear | vedclass

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(A) To find the number of arbitrary constants in the general solution of a differential equation, we need to determine the order of the differential e

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$4$

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(A) To find the number of arbitrary constants in the general solution of a differential equation, we need to determine the order of the differential equation. The number of arbitrary constants is equal to the order of the differential equation.First, we rewrite the given equation to remove the fractional exponent:$\left(\frac{d^4 y}{d x^4}+\frac{d^2 y}{d x^2}\right)^{3 / 2}=5 \frac{d^3 y}{d x^3}$Squaring both sides, we get:$\left(\frac{d^4 y}{d x^4}+\frac{d^2 y}{d x^2}\right)^3 = 25 \left(\frac{d^3 y}{d x^3}\right)^2$The highest order derivative present in the equation is $\frac{d^4 y}{d x^4}$, which is of order $4$.Since the order of the differential equation is $4$, the general solution will contain $4$ arbitrary constants.

The number of arbitrary constants that appear in the general solution of the differential equation $\left(\frac{d^4 y}{d x^4}+\frac{d^2 y}{d x^2}\right)^{3 / 2}=5 \frac{d^3 y}{d x^3}$ is

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