User:Egm6321.f12.team4.hong/Report6

Statement
Find $$y_{xxxxx}$$ in terms of the derivatives of $$y$$ with respect to t where,

Solution
From the above given equations, we can conclude that, Find $$y_{xxxxx}$$ in terms of the derivatives of $$y$$ with respect to t where,

Solving this equations we get,

Author and References

 * Solved and Typed by -- Seong Hyeon Hong
 * Reviewed by --

Statement
Use the IFM to solve,

Recall,

Solution
Rearranging the equation (3)33-3 we get,

Hence, applying equation 2.4.2 and (4)33-3 into equation (1)11-5 we get,

Author and References

 * Solved and Typed by -- Seong Hyeon Hong
 * Reviewed by --

Statement
For the given equation below,

here is the first homogeneous solution,

Show that the second homogeneous solution is,

Solution
Rearranging the equation (2)sec7-1 we get,

It is proven in the lecture note that,

where $$u_1(x)$$ and $$u_2(x)$$ are first and second homogeneous equations respectively.

Therefore if we substitute $$u_1(x)$$ for $$P_2(x)$$ and $$u_2(x)$$ for $$Q_2(x)$$ we get,

The last equation was obtained by the website WolframAlpha.

From the result, it is clear that the result is not same as the given equation. But if we look at the first term of the result and other two given solutions as below,

it seems like there will be a high chance of getting the same $$Q_2(x)$$ if we apply,

Therefore, now $$Q_2(x)$$ becomes,

Again the integration was done by the website WolframAlpha.

Author and References

 * Solved and Typed by -- Seong Hyeon Hong
 * Reviewed by --