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The differential equation of family of circles x2+y2+2λx+c=0, where λ,c both are parameters

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Important Questions on Differential Equations

MEDIUM
The differential equation whose linearly independent solutions are cos2x,sin2x,e-x, is
MEDIUM
The differential equation of all parabolas whose axis is y-axis is
EASY
The order and degree of the differential equation ( y ) 2 + ( y ) 3 ( y ) 4 + y 5 =0 is
HARD
A curve amongst the family of curves represented by the differential equation, x2-y2 dx+2xy dy=0 which passes through 1,1, is
HARD
The solution of the differential equation ydx-x+2y2dy=0 is x=fy. If f-1=1, then f(1) is equal to
HARD
If a curve y=fx passes through the point (1,-1) and satisfies the differential equation, y 1+xydx=x dy, then f-12 is equal to
EASY
The differential equation of the family of curves y=exAcosx+Bsinx , where A and B are arbitrary constants is
HARD
The general solution of the differential equation y2-x3dx-xydy=0, x0 is (where c is a constant of integration)
MEDIUM
The differential equation representing the family of ellipses having foci either on the x-axis or on the y-axis, center at the origin and passing through the point 0,3 is
HARD
Let f:0, πR be a twice differentiable function such that limtxfxsint-ftsinxt-x=sin2x  for all x0,π. If fπ6=-π12, then which of the following statement(s) is (are) TRUE ?
HARD
A solution curve of differential equation x2+xy+4x+2y+4dydx-y2=0, x> passes through the point (1, 3). Then the solution curve -
HARD
Consider the family of all circles whose centers lie on the straight line y=x. If this family of circles is represented by the differential equation Py" + Qy' + 1 = 0,  where P, Q are functions of x, y & y'  y'= dydx, y" = d2ydx2 , then which of the following statements is (are) true ?
MEDIUM

If the differential equation representing the family of all circles touching x-axis at the origin is x2-y2dydx=gxy, then gx equals

HARD
If y=yx satisfies the differential equation 8x9+xdy=4+9+x-1dx and x>0, y0=7, then y256=
MEDIUM
If y=yx is the solution of the differential equation, eydydx-1=ex such that y0=0, then y1 is equal to
HARD
The solution of the differential equation ydx-xdy=xydx is ….
MEDIUM
The solution of the differential equation dydx=tanyx+yx is
EASY
What is the general solution of the differential equation ydx-x+2y2dy=0?
HARD
Let f:RR and g:RR be two non-constant differentiable functions. If fx=efx-gxgx for all xR, and f1=g2=1 then which of the following statement(s) is (are) TRUE?