Class 12

Math

Calculus

Continuity and Differentiability

The solution of the D.E. $cosx(1+cosy)dx−siny(1+sinx)dy=0$ is

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Find a particular solution satisfying the given condition for the following differential equation.$xdxdy −y=gx$, given that $y=0$ when $x=1$.

Find the general solution of each of the following differential equations:$(1+x_{2})dxdy =xy$.

Differentiate the functions with respect to x$cos(cx+d)sin(ax+b) $

Find the equation of a curve passing through the origin given that the slope of the tangent to the curve at any point (x, y) is equal to the sum of the coordinates of the point.

Find the particular solution of the differential equation $xe_{xy}−y+xdxdy =0$ given that $y(e)=0.$

Find the derivative of the function given $byf(x)=sin(x_{2})˙$

Show that the function f defined by $f(x)=∣1−x+x∣,$ where x is any real number, is a continuous function.

Find the general solution for the following differential equation.$xdy+(y−x_{3})dx=0$