Class 12

Math

Calculus

Differential Equations

Find the general solution of the differential equations: $cos_{2}x(dxdy )+y=tanx$ , $(0≤x≤2π )$

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Find the order and degree of the following differential equation: $sin_{−1}(dxdy )=x+y$

Find the curve for which the perpendicular from the foot of the ordinate to the tangent is of constant length.

The curve with the property that the projection of the ordinate on the normal is constant and has a length equal to $a$ is

Show that the differential equation $y_{3}dy+(x+y_{2})dx=0$ can be reduced to a homogeneous equation.

A normal at any point $(x,y)$ to the curve $y=f(x)$ cuts a triangle of unit area with the axis, the differential equation of the curve is

The form of the differential equation of the central conics $ax_{2}+by_{2}=1$ is

Solve the equation $(1−x_{2})(dxdy )+2xy=x1−x_{2} $

What is the integrating factor of the differential equation $(1−y_{2})dydx +xy =ay(−1<y<1)$