MHT CET · Maths · Differential Equations
The order of the differential equation, whose general solution is given by
\(y=\left(\mathrm{c}_1+\mathrm{c}_2\right) \cos \left(x+\mathrm{c}_3\right)-\mathrm{c}_4 \mathrm{e}^{x+\mathrm{c}^5}\)
where \(c_1, c_2, c_3, c_4\) and \(c_5\) are arbitrary constant, is
- A 5
- B 3
- C 4
- D 2
Answer & Solution
Correct Answer
(B) 3
Step-by-step Solution
Detailed explanation
\(\begin{aligned}
y= & \left(c_1+c_2\right) \cos \left(x+c_3\right)-c_4 \mathrm{e}^{x+c^5} \\
= & \left(c_1+c_2\right) \cos \left(x+c_3\right)-c_4 \mathrm{e}^x \mathrm{e}^{c_5} \\
= & A \cos \left(x+c_3\right)-B \mathrm{e}^x \\
\quad & \ldots\left[\mathrm{~A}=c_1+c_2, B=c_4 \mathrm{e}^{c_5}\right]
\end{aligned}\)
There are 3 arbitrary constants.
\(\therefore \quad\) Order of the given differential equation is 3.
y= & \left(c_1+c_2\right) \cos \left(x+c_3\right)-c_4 \mathrm{e}^{x+c^5} \\
= & \left(c_1+c_2\right) \cos \left(x+c_3\right)-c_4 \mathrm{e}^x \mathrm{e}^{c_5} \\
= & A \cos \left(x+c_3\right)-B \mathrm{e}^x \\
\quad & \ldots\left[\mathrm{~A}=c_1+c_2, B=c_4 \mathrm{e}^{c_5}\right]
\end{aligned}\)
There are 3 arbitrary constants.
\(\therefore \quad\) Order of the given differential equation is 3.
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