22e+3y=2;2e-(y)/(2)=(1)/(2))

Directions: In the following questions, A statement of Assertion (A) is followed by a statement of Reason (R). Mark the correct choice as Solution of the differential equation (dy)/(dx)=e^(3x-2y)+x^2e^(-2y) is (e^(2y))/(2)=(e^(3x))/(3)+(x^2)/(2)+C Reason (R) : (dy)/(dx)=e^(3x-2y)+x^2e^(-2y) (dy)/(dx)=e^(-2y)(e^(3x)+x^2) separating the variables e^(2y)dy=(e^(3x)+x^2)dx int e^(2y)dy=int(e^(3x)+x^2)dx (e^(2y))/(2)=(e^(3x))/(3)+(x^3)/(3)+C .

If y(x) is solution of differential equation satisfying (dy)/(dx)+((2x+1)/(x))y=e^(-2x),y(1)=(1)/(2)e^(-2) then (A) y(log_(e)2)=log_(e)2(B)y(log_(e)2)=(log_(e)2)/(4)(C)y(x) is decreasing is (0,1)(D)y(x) is decreasing is ((1)/(2),1)

Solve the differential equation _(y-3)(dy)/(dx)=((x+1)^(2)+(y-3)^(2)e^((y-3)/(x-1)))/((xy-3x+y-3)e^(x+1))

e_(1),e_(2),e_(3),e_(4) are eccentricities of the conics xy=c^(2),x^(2)-y^(2)=c^(2),(x^(2))/(a^(2))-(y^(2))/(b^(2))=1,(x^(2))/(a^(2))-(y^(2))/(b^(2))=-1 and sqrt((1)/(e_(1)^(2))+(1)/(e_(2)^(2))+(1)/(e_(3)^(2))+(1)/(e_(4)^(2)))=sec theta then 2 theta is

Let y=y(x) be the solution of the differential equation,x((dy)/(dx))+y=x log_(e)x,(x>1) if 2y(2)=log_(e)4-1, then y(e) is equal to: (a)-((e)/(2))(b)-((e^(2))/(2))(c)(e)/(4)(d)(e^(2))/(4)

If the curve satisfying (1+e^((x)/(y)))dx+e^((x)/(y))(1-(x)/(y))dy=0 passes through (1,1) then 9+y(2)e^((2)/(y(2)))-e is equal to-

If e and e' are the eccentricities of the hyperbola (x^(2))/(a^(2))-(y^(2))/(b^(2)) =1 and (y^(2))/(b^(2))-(x^(2))/(a^(2))=1 , then the point ((1)/(e),(1)/(e')) lies on the circle:

If e and e' are the eccentricities of the hyperbola (x^(2))/(a^(2))-(y^(2))/(b^(2)) =1 and (y^(2))/(b^(2))-(x^(2))/(a^(2))=1 , then the point ((1)/(e),(1)/(e')) lies on the circle:

If x=(e^(y)-e^(-y))/(e^(y)+e^(-y)) show that y=1/2log_(e )((1+x)/(1-x))

If y = (e^(x)-e^(-x))/(e^(x)+e^(-x)) then prove that y = (e^(2x)-1)/(e^(2x)+1) .