Class 12

Math

Calculus

Differential Equations

Form the differential equation of the family of circles in the second quadrant and touching the coordinate axes.

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Determine order and degree (if defined) of differential equations given$yprime+5y=0$

Verify that the given functions (explicit or implicit) is a solution of the corresponding differential equation:$ycosy=x$ : (y sin y + cos y + x) y = y

Find the general solution of the differential equations $dxdy =4−y_{2} $ , $(−2<y<2)$

Find the particular solution of the differential equation $dxdy +ycotx=2x+x_{2}cotx(x=0)$given that $y=0$when $x=2π $.

Find the particular solution of the differential equation $g(dxdy )=3x+4y$ given that $y=0$ when $x=0$.

A homogeneous differential equation of the from $dydx =h(yx )$can be solved by making the substitution.(A) $y=vx$ (B) $v=yx$ (C) $x=vy$ (D) $x=v$

The differential equations, find a particular solution satisfying the given condition: $x(x_{2}−1)dxdy =1;y=0$when $x=2$

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