Class 12

Math

Calculus

Differential Equations

Form the differential equation of the family of circles touching the x-axis at origin.

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In a bank, principal increases continuously at the rate of 5% per year. In how many years Rs 1000 double itself?

In a bank, principal increases continuously at the rate of r% per year. Find the value of r if Rs 100 double itself in 10 years $(g_{e}=0.6931)$

The volume of spherical balloon being inflated changes at a constant rate. If initially its radius is 3 units and after 3 seconds it is 6 units. Find the radius of balloon after t seconds.

Find a particular solution of the differential equation $dydx +ycotx=1(x=0)4xcosecx$$(x=0)$, given that $y=0$when $x=2π $

Find the general solution of the differential equations $(e_{x}+e_{−x})dy−(e_{x}−e_{−x})dx=0$

Find the equation of a curve passing through the point $(0,2)$given that at any point (x, y) on the curve, the product of the slope of its tangent and y coordinate of the point is equal to the x coordinate of the point.

Show that the differential equation $2ye_{yx}dx+(y−2xe_{yx})dy=0$ is homogeneous and find its particular solution, given that, $x=0$when$y=1$.

The Integrating Factor of the differential equation $(1−y_{2})dydx +yx=ay$ , $(−1<y<1)$is(A) $y_{2}−11 $ (B) $y_{2}−1 1 $ (C) $1−y_{2}1 $ (D) $1−y_{2} 1 $