PYQSidePowered by
ExamsMy practice
The solution curve of the differential equation y dxdy=x ( e x- e y+1 ), x>0, y>0 passing through the point (e, 1) is
(3) | e xy |=y
dxdy= xy ( e xy+1 ) is homogeneous ⇒ put x=ty, dxdy=t+y dtdy
t+y dtdy=t e t+t
dtt e t= dyy
e | e t |= e y+c
at (e, 1): t=e ⇒ e 1=0+c ⇒ c=0
| e xy |=y
Answer: (3)
The temperature T(t) of a body at time t=0 is 160 F and it decreases continuously as per the differential equation dTdt=-K(T-80), where K is a positive constant. If T(15)=120 F, then T(45) is equal to
Let y=y(x) be the solution of the differential equation 2x dx+ (e2y 2x+ x )dy=0, 0<x< 2, y( /4)=0. If y( /6)= , then e8 is equal to .
Let y=y(x) be the solution of the differential equation x dy+\2(1-x) x+x(2-x)\dx=0 such that y(0)=2. Then y(2) is equal to:
Let y=y(x) be the solution of the differential equation (1-x2 )dy= [xy+ (x3+2 ) 3 (1-x2 ) ]dx, -1<x<1, y(0)=0. If y ( 12 )= mn, m and n are co-prime numbers, then m+n is equal to .
Let Y=Y(X) be a curve lying in the first quadrant such that the area enclosed by the line Y-y=Y (x)(X-x) and the co-ordinate axes, where (x, y) is any point on the curve, is always -y22 Y (x)+1, Y (x) 0. If Y(1)=1, then 12 Y(2) equals .
A function y=f(x) satisfies f(x) 2x+ x- (1+ 2x )f'(x)=0 with condition f(0)=0. Then, f ( 2 ) is equal to
If the solution curve y=y(x) of the differential equation (1+y2 ) (1+ ex )dx+x dy=0, x>0 passes through the point (1,1) and y(e)= - ( 32 ) + ( 32 ), then +2 is .
If ( yx )= e|x|+ 2 is the solution of the differential equation x ( yx ) dydx=y ( yx )+x and y(1)= 3, then 2 is equal to
Let f(x)= r x \ 2r2 [(f(r))2-f(x)f(r) ]r2-x2-r3e f(r)r \ be differentiable in (- , 0) (0, ) and f(1)=1. Then the value of ea, such that f(a)=0, is equal to .
Let x=x(t) and y=y(t) be solutions of the differential equations dxdt+ax=0 and dydt+by=0 respectively, a, b . Given that x(0)=2; y(0)=1 and 3y(1)=2x(1), the value of t, for which x(t)=y(t), is :