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Confused....
Ok, ok.... I totally don't get this....
Lets deal with the RHS first, they're integrating t^2 with respect to t, should that not be (1/3).t^3 + C???
And the LHS, where the hell did dx come from?! How did they get the integral on the LHS?!
I'm hopeless....
Lets deal with the RHS first, they're integrating t^2 with respect to t, should that not be (1/3).t^3 + C???
And the LHS, where the hell did dx come from?! How did they get the integral on the LHS?!
I'm hopeless....
The dx was probably a mistake. The y (with the dot) implies
So it really should have been dy.
And yes, they did intergrate the RHS, but they simplified it. Try it yourself, and multiply by 6. You will get the correct anwser.
So it really should have been dy.
And yes, they did intergrate the RHS, but they simplified it. Try it yourself, and multiply by 6. You will get the correct anwser.
Remember y(dot) = dy/dt
so the question is dy/dt = t^2/(y + e^y)
Separating variables (ie putting all of one variable on one side of the equation and treating the differential symbol as a fraction) and putting in the integral signs we get
Int (y + e^y ) dy = Int (t^2) dt
So (1/2)y^2 + e^y = (1/3)t^3 + c
Multiplying through by 3 gives
(3/2)y^2 + 3e^y = t^3 +c
Multiplying through by 2 gives:
3y^2 + 6e^y = 2t^3 + c
(I'm assuming here you understand the method of integration by separating variables, so I've just explain what you do in practice, rather than why we do it and why it works
)
so the question is dy/dt = t^2/(y + e^y)
Separating variables (ie putting all of one variable on one side of the equation and treating the differential symbol as a fraction) and putting in the integral signs we get
Int (y + e^y ) dy = Int (t^2) dt
So (1/2)y^2 + e^y = (1/3)t^3 + c
Multiplying through by 3 gives
(3/2)y^2 + 3e^y = t^3 +c
Multiplying through by 2 gives:
3y^2 + 6e^y = 2t^3 + c
(I'm assuming here you understand the method of integration by separating variables, so I've just explain what you do in practice, rather than why we do it and why it works
)Roger Kirk
Remember y(dot) = dy/dt
so the question is dy/dt = t^2/(y + e^y)
Separating variables (ie putting all of one variable on one side of the equation and treating the differential symbol as a fraction) and putting in the integral signs we get
Int (y + e^y ) dy = Int (t^2) dt
So (1/2)y^2 + e^y = (1/3)t^3 + c
Multiplying through by 3 gives
(3/2)y^2 + 3e^y = t^3 +c
Multiplying through by 2 gives:
3y^2 + 6e^y = 2t^3 + c
(I'm assuming here you understand the method of integration by separating variables, so I've just explain what you do in practice, rather than why we do it and why it works)
so the question is dy/dt = t^2/(y + e^y)
Separating variables (ie putting all of one variable on one side of the equation and treating the differential symbol as a fraction) and putting in the integral signs we get
Int (y + e^y ) dy = Int (t^2) dt
So (1/2)y^2 + e^y = (1/3)t^3 + c
Multiplying through by 3 gives
(3/2)y^2 + 3e^y = t^3 +c
Multiplying through by 2 gives:
3y^2 + 6e^y = 2t^3 + c
(I'm assuming here you understand the method of integration by separating variables, so I've just explain what you do in practice, rather than why we do it and why it works
)Yeah I do, I just haven't slept and thus I was trying to integrate with respect to x, blindly following the question..... Thanks tho!!
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