solve the differential equation: x*y*(dy/dx) = 3x^2 + y^2 i have real problems with differential equations so if anyone could give a brief method or some reasoning id really appreciate it. Thanks
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If you express it in the form dy / dx + ay = f(x) you can use the integrating factor method.
Originally Posted by snowmonkey12 solve the differential equation: x*y*(dy/dx) = 3x^2 + y^2 x y y' = 3x^2 + y^2 y' = (3x^2 + y^2) / (x y) y' = 3x/y + y/x y' - y/x = 3x/y (x y' - y) / x = 3x/y (y/x)' x = 3x/y (y/x)' = 3/y Let y = u x , u' = 3 / (u x) u du = 3 dx / x u^2 = 6 ln |x| + 2C y^2 = 6 x^2 ln |x| + 2 C x^2
Oh of course, yes. It's homogeneous. Sorry for my previous posting. It was rubbish.
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