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Find the general solution for the equation:
Solution:
The equation above is Differential Equation because it has dx and dy. The type of equation is Homogeneous because the functions and variables cannot be separated by Separation of Variables. There's a method to solve the Homogeneous Functions. Consider the given equation
Let y = vx
dy = vdx + xdv
Substitute y and dy to the given equation, we have
The above equation can now be separated by Separation of Variables. Divide both sides of the equation by x2.
Integrate both sides of the equation
but y = vx and v = y/x, therefore,
Multiply both sides of the equation by 4x,
