The differential equation of all circles passing through the origin and having their centres on the x-axis is
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Solve the differential equation [xe−2x−xy]dydx=1(x=0)
Form a differential equation representing the given family of curves by eliminating arbitrary constants a and b.y=ae3x+be−2x
Show that the given differential equation is homogeneous and solve each of them.(x2+xy)dy=(x2+y2)dx
Show that the differential equation (x−y)dxdy=x+2yis homogeneous and solve it.
Find the general solution of the differential equations (ex+e−x)dy−(ex−e−x)dx=0
Solve the differential equation (tan−1y−x)dy=(1+y2)dx.
The differential equations , find the particular solution satisfying the given condition:2xy+y2−2x2dxdy=0;y=2when x = 1
Verify that the given functions (explicit or implicit) is a solution of the corresponding differential equation: y=1+x2: y′=1+x2xy y=Ax : xy′=y(x=0)