Statement-I: The order of the differential equation whose primitive is y = A +ℓ nBx is 2 because Statement-II: If there are ' n ' independent arbitrary constants in a family of curve then the order of the corresponding differential equation is ' n '.

Question

Statement-I: The order of the differential equation whose primitive is y = A +ℓ nBx is 2 because Statement-II: If there are ' n ' independent arbitrary constants in a family of curve then the order of the corresponding differential equation is ' n '. (A) Statement-I is true, Statement-II is true ; Statement-II is correct explanation for Statement-I. (B) Statement-I is true, Statement-II is true ; Statement-II is NOT a correct explanation for statement-I. (C) Statement-I is true, Statement-II is false. (D) Statement-I is false, Statement-II is true.

Tardigrade Admin · Accepted Answer

y = A + ln Bx ∴ ( dy / dx )=(1/ x ) Hence order is 1 . So statement-I is false statement-II is true.

Q. Statement-I : The order of the differential equation whose primitive is $y = A + ℓ n B x$ is 2 because
Statement-II : If there are ' $n$ ' independent arbitrary constants in a family of curve then the order of the corresponding differential equation is ' $n$ '.

Statement-I is true, Statement-II is true ; Statement-II is correct explanation for Statement-I.

Statement-I is true, Statement-II is true ; Statement-II is NOT a correct explanation for statement-I.

Statement-I is true, Statement-II is false.

Statement-I is false, Statement-II is true.

$y = A + ln B x$
$∴ \frac{d y}{d x} = \frac{1}{x}$
Hence order is 1 .
So statement-I is false \& statement-II is true.

Q. Statement-I : The order of the differential equation whose primitive is y=A+ℓnBx is 2 because Statement-II : If there are ' n ' independent arbitrary constants in a family of curve then the order of the corresponding differential equation is ' n '.