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A day full of math games & activities. Find one near you.
Find the general solution of the given higher-order differential equation. y'''-6y''-7y' = 0
Solution:
The characteristic equation of the given differential equation is as follows:
r3 - 6r2 - 7r = 0
Taking r common we have
r(r2 - 6r -7) = 0
Factorising (r2 - 6r -7) we get
r(r - 7)(r + 1) = 0
And so the characteristic equation has three distinct real roots r = 0, r = -1, and r = 7.
The general solution can be written as :
y(x) = \( c_{1}e^{0.x} + c_{2}e^{-1x}+ c_{2}e^{7x} \)
Now we know that e0 =1
y(x) = \( c_{1} + c_{2}e^{-1x}+ c_{2}e^{7x} \)
The above equation is the general solution of the given equation.
Find the general solution of the given higher-order differential equation. y'''-6y''-7y' = 0
Summary:
The general solution to the third order linear differential equation is : y(x) = \( c_{1} + c_{2}e^{-1x}+ c_{2}e^{7x} \)
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