INTRODUCTIONFamily of curves, Differential

equations from a family of curves

Family of Curves

FAMILY OF CURVES A family of curves is a set of curves which

can be represented by a single equation. But this equation is not defined explicitly. Instead it is defined in a way that includes arbitrary constants or parameters.

Family of curves

Family of curves

Family of Curves

Differential Equation From a Family of Curves

DIFFERENTIAL EQUATION A differential equation is an equation that

contains derivatives. These could be ordinary derivatives or partial derivatives.

Differential Equations from a Family of Curves

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Differential Equations from a Family of Curves

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Differential Equations from Family of Curves

Differential Equations from a Family of Curves

Differential Equations from a Family of Curves

Differential Equation from a Family of Curves

Differential Equations from a Family of Curves

Solved Problems 1.4Obtain the differential equation from the family of curves described by the following equations.