9) If the general solution of some differential equation is \( y=a_{1}\left(a_{2}+a_{3}\right) \cdot \cos \left(x+a_{4}\right)-a_{3} e^{x+a_{0}} \) then order of differential equation is \( \begin{array}{ll}\text { (A) } 5 & \text { (B) } 4 \\ \text { (C) } 6 & \text { (D) } 3\end{array} \)
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The general solution you provided involves various terms: constants \( a_1, a_2, a_3, a_4 \), a trigonometric function \( \cos(x + a_4) \), and an exponential function \( e^{x + a_0} \). Each arbitrary constant in a general solution of a differential equation often corresponds to an order of the equation. Since there are four constants, the differential equation is of order 4. It’s essential to remember that the order of a differential equation reflects the number of arbitrary constants in its general solution. In this case, with four constants at play, the answer is clear as a sunny day!
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