Class 12

Math

Calculus

Differential Equations

Show that the differential equation $dx(x−y)dy =x+2y,$is homogeneous and solve it.

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The differential equations , find the particular solution satisfying the given condition: $(x+y)dy+(x–y)dx=0;y=1$ when $x=1$

Verify that the given functions (explicit or implicit) is a solution of the corresponding differential equation:$x+y=tan_{−1}y$ : $y_{2}y_{prime}+y_{2}+1=0$

Verify that the given functions (explicit or implicit) is a solution of the corresponding differential equation:$y=cosx+C$ : $yprime+sinx=0$

Find the general solution of the differential equations $dxdy =1+cosx1−cosx $

Form a differential equation representing the given family of curves by eliminating arbitrary constants a and b.$ax +by =1$

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

Form the differential equation representing the family of curves $y=mx$, where, m is arbitrary constant.

Show that the family of curves for which the slope of the tangent at any point (x, y) on it is $2xyx_{2}+y_{2} $, is given by $x_{2}−y_{2}=cx$.