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Step by Step Explanation of Differential Equations

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I am asking for the step-by-step workings for all of the attached problems.
** Please see the attached file for complete problem description **

1st problems. Please find the general solution of:
(1) dy/dx = y/sin(y) - x
(2) dy/dx = y + cos(x)y^2010
In the process of finding the solutions for the problems make use of both the method of
variation of constants and integrating factor. Explain similarities and differences.
2.i problems. Please find the general solutions of:
(1) dy/dx = y + cos^2(x)y^3
(2) dy/dx = xy +x
Use the method of variation of constants in the process of finding solutions for problem
(1). Use the method of integrating factor for
2.ii problems. Please the general solutions of:
(1) dy/dx = y + x
(2) dy/dx = -y + e^x
Use the method of variation of constants.

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https://brainmass.com/math/calculus-and-analysis/step-step-explanation-differential-equations-511161

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** Please see the attached file for the complete solution **
I used other methods besides variation of parameters to solve these - I hope this is OK. (I've never seen variation of parameters used for first order differential equations in any case - this method is usually used for second or higher orders.)

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Solution Summary

The solution solves several first order ordinary differential equations using various methods.

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Differential Equation and Unit Step: Analytic Solution

Consider the differential equation

(d^2y/dt^2) + 3(dy/dt) + 2y = u

where y(0)=dy(0)/dt and u(t) is a unit step.

1. Determine the solution y(t) analytically.

Please Show all steps and explanation of each step
Thank You

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