Class 12

Math

Calculus

Differential Equations

Find the differential equation representing the family of curves $y=ae_{bx+5}$, where a and b are arbitrary constants.

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Find the general solution of the differential equations:$(x+y)dydx =1$

$ydx+(x−y_{2})dy=0$

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

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

Find the general solution of the differential equations:$dydx +secxy=tanx(0≤x<2π )$

Find the general solution of the differential equations $e_{x}tanydx+(1−e_{x})sec_{2}ydy=0$

Solve the differential equation $[x e_{−2x} −x y ]dydx =1(x=0)$