Question:
The order of the differential equation whose general solution is
\[
y=a\sin x+b\cos x
\]
where \(a\) and \(b\) are arbitrary constants, is
The order of the differential equation whose general solution is
\[
y=a\sin x+b\cos x
\]
where \(a\) and \(b\) are arbitrary constants, is
Show Hint
Number of arbitrary constants in the general solution equals the order of the differential equation.
Updated On: May 7, 2026
- \(2\)
- \(4\)
- \(1\)
- \(3\)
Show Solution
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The Correct Option is A
Solution and Explanation
Step 1: Given general solution: \[ y=a\sin x+b\cos x \]
Step 2: It contains two arbitrary constants: \[ a,\quad b \]
Step 3: The order of the differential equation is equal to the number of arbitrary constants in its general solution.
Step 4: Therefore, order is: \[ 2 \] \[ \boxed{2} \]
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