Show that the following differential equation is a homogeneous differential equation and then find its solution. xyy' + 4x^2 + y^2 = 0 , y(2) = -7
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The given differential equation is xyy + 4x^2 + y^2 = 0. We can rewrite this as y(dy/dx) = -4x - y^2/x. Here, the right-hand side is a function of x and y, and it is homogeneous of degree 1, because if we replace x with tx and y with ty, we get -4tx - Show more…
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