IIT JEE , AIEEE Forum - Mathematics , Integral Calculus

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A second order linear homogeneous ordinary differential equation with constant coefficients can be expressed as

a₂y" + a₁y' +a₀ y =0

This equation implies that the solution is a function whose derivatives keep the same form as the function itself and do not explicitly contain the independent variable x, since constant coefficients are not capable of correcting any irregular formats or extra variables. An elementary function which satisfies this restriction is the exponential function

Substitute the exponential function

into the above differential equation, the characteristic equation of this differential equation is obtained

a_2² + a₁ +a₀ =0

This characteristic equation has two roots

_¹ and

_²

2nd Order Linear Homogeneous ODE with Constant Coefficients:
Characteristic Equation:
Solutions of Characteristic Equation ,		General Solution
1
2
3

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