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Differential Equations — Maths STD 12 Science — Question

Gujarat BoardEnglish MediumSTD 12 ScienceMathsDifferential Equations1 Mark
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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