Question

Obtain the differential equation by eliminating the arbitrary constants from the following equation:

y = c₁e^2x + c₂e^5x

Answer 1

y = c₁e^2x + c₂e^5x .......(1)

Differentiating twice w.r.t. x, we get

The equations (1), (2) and (3) are consistent in c₁e^2x + c₂e^5x

∴ determinant of their consistency is zero.

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This is the required D.E.

Alternative Method:

y = c₁e^2x + c₂e^5x

Dividing both sides by e^5x ,we get

Differentiating w.r.t. x, we get

Dividing both sides by e^-3x, we get

Differentiating w.r.t. x, we get

This is the required D.E.