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VladimirAG [237]
3 years ago
12

Find the general solution of the differential equation and check the result by differentiation. (Use C for the constant of integ

ration.) dy dt = 27t8
Mathematics
1 answer:
tensa zangetsu [6.8K]3 years ago
4 0

Answer:

y=3t^9+C

Step-by-step explanation:

Given:  \dfrac{dy}{dt}=27t^8

We want to obtain the general solution of the given differential equation.

dy=27t^8$ dt\\$Take the integral of both sides\\\int dy =\int 27t^8$ dt$\\y=\dfrac{27t^{8+1}}{8+1} +C$, (where C is the constant of integration)$\\y=\dfrac{27t^{9}}{9} +C\\\\y=3t^9+C

The general solution of the differential equation is: y=3t^9+C

CHECK:

\dfrac{d}{dt} y=\dfrac{d}{dt}(3t^9+C)=\dfrac{d}{dt}(3t^9)+\dfrac{d}{dt}(C)\\\\\text{Since derivative of a constant is zero}\\\\\dfrac{dy}{dt}=27t^{9-1}\\\dfrac{dy}{dt}=27t^8

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