Class 12

Math

Calculus

Differential Equations

Find the general solution of the differential equation $dxdy −y=cosx$

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Show that the given differential equation is homogeneous and solve each of them.$xdxdy −y+xsin(xy )=0$

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

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) $x=v$

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

Verify that the function $y=c_{1}e_{ax}cosbx+c_{2}e_{ax}sinbx$, where $c_{1},c_{2}$are arbitrary constants is a solution of the differential equation. $dx_{2}d_{2}y −2adxdy +(a_{2}+b_{2})y=0$

Determine order and degree (if defined) of differential equations given$dx_{2}d_{2}y =cos3x+sin3x$

Find the equation of a curve passing through the point $(2,3)$, given that the slope of the tangent to the curve at any point (x, y) is $y_{2}2x $.

Find the general solution of the differential equation $xdxdy +2y=x_{2}(x=0)$.