Assertion (A) : Order of the differential equation whose solution… - Vidyadip

MCQ

Assertion (A) : Order of the differential equation whose solution is $y=c_1 e^{x+c_2}+c_3 e^{x+c_4}$ is 4.
Reason (R) : Order of the differential equation is equal to the number of independent arbitrary constants mentioned in the solution of the differential equation.

A
Both (A) and (R) are true and (R) is the correct explanation of (A).
B
Both (A) and (R) are true but (R) is not the correct explanation of (A).
C
(A) is true but (R) is false.
✓
(A) is false but (R) is true.

✓

Answer

Correct option: D.

(A) is false but (R) is true.

(d): $\because y=\left(c_1 e^{c_2}+c_3 e^{c_4}\right) e^x=c e^x$ ...(i)
Solution of differential equation containing the arbitrary constant.
$\therefore \quad$ Order is 1.

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