Q. 15

Write the order of the differential equation whose solution is y = a cos x + b sin x + c e–x.

Answer :

Solution of differential equation is


y = a cos x + b sin x + c e–x ---(1)


Since it has 3 constants a, b, c we differentiate it by 3 times


Differentiate w.r.t x we get,


---(2)


Again, differentiate w.r.t x we get,


---(3)


Again, differentiate w.r.t x we get,


---(4)


Equation (3) implies


From (1)



---(5)


Now, adding equation (2) and (4) we get,





is the required differential equation.


Here the order of differential equation is 3.


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