The order of the differential equation,whose | vedclass

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(B) Given the general solution: $y = (c_1 + c_2) \cos (x + c_3) - c_4 e^{x + c_5}$.We can simplify the expression by grouping the constants:Let $A = c

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$3$

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(B) Given the general solution: $y = (c_1 + c_2) \cos (x + c_3) - c_4 e^{x + c_5}$.We can simplify the expression by grouping the constants:Let $A = c_1 + c_2$ and $B = c_4 e^{c_5}$.Then the equation becomes $y = A \cos (x + c_3) - B e^x$.Expanding the cosine term: $y = A (\cos x \cos c_3 - \sin x \sin c_3) - B e^x$.$y = (A \cos c_3) \cos x - (A \sin c_3) \sin x - B e^x$.Let $K_1 = A \cos c_3$,$K_2 = -A \sin c_3$,and $K_3 = -B$.Thus,$y = K_1 \cos x + K_2 \sin x + K_3 e^x$.There are $3$ independent arbitrary constants $(K_1, K_2, K_3)$.The order of a differential equation is equal to the number of independent arbitrary constants in its general solution.Therefore,the order of the differential equation is $3$.

The order of the differential equation,whose general solution is given by $y = (c_1 + c_2) \cos (x + c_3) - c_4 e^{x + c_5}$,where $c_1, c_2, c_3, c_4$ and $c_5$ are arbitrary constants,is

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