Definition:
Homogeneous differential equation is a type of differential equation. A differential equation is a equation which contains derivatives. Homogeneous differential equation also contains derivatives of functions in it.
Formula: y'=f(x,y). If f(x, y) is a homogeneous function of degree 0,
Example:
Find the First Order ODE for x2+cosx+2x+5=0
Solution:
Integerate the give equation once.
∫(x2+cosx+2x+5) = ∫x2+∫cosx+∫2x+∫5
∫(x2+cosx+2x+5) = (1/3)x3+sinx+(2/2)x2+5x+C
∫(x2+cosx+2x+5) = (1/3)x3+sinx+x2+5x+C
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