# Solutions to various differential equations

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

https://brainmass.com/math/calculus-and-analysis/solutions-various-differential-equations-61800

#### Solution Preview

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

Solve the following differential equations:

i)

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 ...

#### Solution Summary

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