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Solutions to various differential equations

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Please find the attachment for the questions.
Five Linear Homogeneous Differential equations that are to be solved using Variables separable and other standard methods are given in the attachment

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Solution Summary

The solutions are provided to various differential equations using variables separable method and other standard methods to solve homogeneous, linear differential equations.

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Please see the attached files for the detailed and step by step solutions.

Solve the following differential equations:


This is a homogeneous equation, as the total degree of x and y in each term is same, 4.
In such problems, we substitute y=xv, which gives

Using this relation in (i), we get

Using the variables separable method, we can write

Integrating on both sides, we get

Substituting the ...

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