Ans it plzzz........“Under what conditions an nth order non - homogeneous linear differential equation (initial value problem) have a unique solution?”  

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sciencesolve | Teacher | (Level 3) Educator Emeritus

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Consider the linear nonhomogeneous differential equation

`y" + r(t)y' + s(t)y = h(t)`

You need to remember that the structure of general solution to  linear nonhomogeneous differential equation is:

`y(t) = y_r(t) + c_1*y_1(t) + c_2*y_2(t)`

`c_1; c_2`  denote constants

`y_1(t);y_2(t)`  denote fundamental solutions to the equation `y" + r(t)y' + s(t)y = 0`

`y_r(t) ` denotes a particular solution to nonhomogeneous differential equation

Hence, evaluation of solution to nonhomogeneous differential equation needs you to follow the next algorithm: finding the general solution to `y" + r(t)y' + s(t)y = 0`  and finding the unique solution to`y" + r(t)y' + s(t)y = h(t)` , then combine these two solutions together.

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