Class 12

Math

Calculus

Differential Equations

The function f(θ)=ddθ∫0θdx1−cosθcosx satisfies the differential equation

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Form the differential equation of all circle touching the x-axis at the origin and centre on the y-axis.

The differential equation which represents the three parameter family of circlesx2+y2+2gx+2fy+c=0 is

Solve $dxdy 1+x+y =x+y−1$

Solve $x(dxdy )=y(gy−gx+1)$

The differential equation of family of curves whose tangent form an angle of π/4 with the hyperbola xy=C2 is

Solve the equation $ydx+(x−y_{2})dy=0$

The solution to the differential equation $ygy+xy_{prime}=0,$ where $y(1)=e,$ is

The differential equation of the curve for which the initial ordinate of any tangent is equal to the corresponding subnormal (a) is linear (b) is homogeneous of second degree (c) has separable variables (d) is of second order