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If \(c_1, c_2, c_3, c_4, c_5\) are arbitrary constants, then the order of the differential equation whose general solution is \(y=\left(c_1+c_2\right) \sin \left(x+c_3\right)+c_4 e^{x+c_5}\) is
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Verified Answer
The correct answer is:
3
General solution of differential equation is,
\(y=\left(C_1+C_2\right) \sin \left(x+C_3\right)+C_4 e^{x+C_5}\)
Here solution is of form;
\(\begin{aligned}
& y=A \sin \left(x+C_3\right)+B e^x \\
& {\left[\because C_1+C_2=A, C_4 e^c=B\right] }
\end{aligned}\)
So, there are 3-arbitrary constants, \(A_1 C_3\) and \(B\) Now, order of differential equation \(=\) number of arbitrary constants in general solution.
So, order of differential equation is 3.
\(y=\left(C_1+C_2\right) \sin \left(x+C_3\right)+C_4 e^{x+C_5}\)
Here solution is of form;
\(\begin{aligned}
& y=A \sin \left(x+C_3\right)+B e^x \\
& {\left[\because C_1+C_2=A, C_4 e^c=B\right] }
\end{aligned}\)
So, there are 3-arbitrary constants, \(A_1 C_3\) and \(B\) Now, order of differential equation \(=\) number of arbitrary constants in general solution.
So, order of differential equation is 3.
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