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# A general second order linear differential equation with constant coefficients is of the form

Second Order first degree differential equations with constant coefficients

Second Order first degree differential equations with constant coefficients

A general second order linear differential equation with constant coefficients is of the form where ϕ(D) = aD2 + bD + c (a,b and c are constants)

To solve the equation (1), we first solve the equation ϕ ( D ) y = 0. The solution so obtained is called complementary function (C.F).

Next we operate on f ( x) with 1/ ϕ ( D) , the solution so obtained is called particular integral (P.I) Type 1 : f(x) = 0

(i.e) ϕ(D)y = 0

To solve this, put ϕ ( D) = 0

Replace D by m. This equation is called auxiliary equation . ϕ( m ) = 0 is a quadratic equation. So we have two roots, say m1 and m2.

Now we have the following three cases Here A and B are arbitrary constants

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12th Business Maths and Statistics : Chapter 4 : Differential Equations : A general second order linear differential equation with constant coefficients is of the form |