Homogeneous differential equation

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A differential equation can be homogeneous in either of two respects. A first order differential equation is said to be homogeneous if it may be written f ( x , y ) d y = g ( x , y ) d x , {\displaystyle f(x,y)\,dy=g(x,y)\,dx,} where f and g are homogeneous functions of the same degree of x and y. In this case, the change of variable y = ux leads to an equation of the form d x x = h ( u ) d u , {\displaystyle {\frac {dx}{x}}=h(u)\,du,} which is easy to solve by integration of the two members. Otherwise, a differential equation is homogeneous if it is a homogeneous function of the...

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