Consider the differential equation (x y-1) (d y/d x)+y2=0 Statement-I: The solution of the equation is xy = log y+ c. because Statement-II: The given differential equation can be expressed as ( dx / dy )+ Px = Q, whose integrating factor is ℓ ny.

Question

Consider the differential equation (x y-1) (d y/d x)+y2=0 Statement-I: The solution of the equation is xy = log y+ c. because Statement-II: The given differential equation can be expressed as ( dx / dy )+ Px = Q, whose integrating factor is ℓ ny. (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

Correct answer is (c) Statement-I is true, Statement-II is false.

Q. Consider the differential equation (xy−1)dxdy​+y2=0 Statement-I : The solution of the equation is xy=logy+c. because Statement-II : The given differential equation can be expressed as dydx​+Px=Q, whose integrating factor is ℓ ny.

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.

Correct answer is (c) Statement-I is true, Statement-II is false.

Q. Consider the differential equation $(x y - 1) \frac{d y}{d x} + y^{2} = 0$
Statement-I : The solution of the equation is $x y = lo g y + c$ . because
Statement-II : The given differential equation can be expressed as $\frac{d x}{d y} + P x = Q$ , whose integrating factor is $ℓ$ ny.