Question #349888

x^2dy/dx-3y^4=2xy

Expert's answer

Let "u=y^3." Then "u'=3y^2y'"

"3x^2y^2y'-9y^6=6xy^3""x^2u'-6xu=9u^2"

"u'-\\dfrac{6}{x}u=\\dfrac{9}{x^2}u^2"

Bernoulli Equation

"z'=-u^{-2}u'"

"z'+\\dfrac{6}{x}z=-\\dfrac{9}{x^2}"

"x^6z'+6x^5z=-9x^4"

"d(x^6z)=-9x^4dx"

"z=\\dfrac{C-9x^5}{5x^6}"

"y^3=\\dfrac{5x^6}{C-9x^5}"

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