Assume , , and are arbitrary constants, find a DE which is a general solution of the given expression whose order is equal to the number of arbitrary constants in the expression.
y= 2ax + bx^2
(x-a)^2 + (y-b)^2=c^2
y=ae^-x + (b/x)
y= ae^2x + be^3x+ x^3
y=asin5x + bcos5x
Find the D.E. for the given family of curves. Sketch representative family of curves.
6. All circles of radius 1 unit.
7. Family of lines passing through (-2,0).
8. Family of parabolas having their vertices on the origin and focus on the y-axis.
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