class 12

Math

Calculus

Differential Equations

A curve passes through the point $(1,6π )$ . Let the slope of the curve at each point $(x,y)$ be $xy +sec(xy ),x>0.$ Then the equation of the curve is

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Verify that the function $y=e_{−3x}$is a solution of the differential equation $dx_{2}d_{2}y +dxdy −6y=0$

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

The differential equations, find a particular solution satisfying the given condition: $cos(dxdy )=a(a∈R);y=1$

Verify that the given function (implicit or explicit) is a solution of the corresponding differential equation.(i) $y=ae_{x}+be_{−x}+x_{2}$ : $xdx_{2}d_{2}y +2ydxdy −xy+x_{2}−2=0$

Show that the given differential equation is homogeneous and solve each of them. $(x–y)dy–(x+y)dx=0$

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

Solve the differential equation $(tan_{−1}y−x)dy=(1+y_{2})dx$.

Find the general solution of the differential equations $dxdy =(1+x_{2})(1+y_{2})$