Class 12

Math

Calculus

Differential Equations

Write the differential equation obtained by eliminating the arbitrary constant C in the equation representing the family of curves $xy=Ccosx˙$

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Show that the differential equation $xcos(xy )dxdy =ycos(xy )+x$is homogeneous and solve it.

Verify that the given functions (explicit or implicit) is a solution of the corresponding differential equation:$y=x_{2}+2x+C$ : $yprime−2x−2=0$

Solve the following differential equation : $xcosydy=(xe_{x}gx+e_{x})dx$

If $y(x)$ is solution of \displaystyle{x}\frac{{{\left.{d}{y}\right.}}}{{{\left.{d}{x}\right.}}}+{2}{y}={x}^{{{2}}},{y}

Solve the following differentia equation: $(y_{2}−x_{2})dy=3x ydx$

Find the equation of a curve passing through the point (0, 2) given that the sum of the coordinates of any point on the curve exceeds the magnitude of the slope of the tangent to the curve at that point by 5.

If a curve $y=f(x)$ passes through the point $(1,−1)$ and satisfies the differential equation $,y(1+xy)dx=xdy$ , then $f(−21 )$ is equal to:(A) $−52 $ (B) $−54 $ (C) $52 $ (D) $54 $

The differential equations, find a particular solution satisfying the given condition: $dydx +2ytanx=sinx;y=0$when $x=3π $