I have tried the solve following differential equation with Riccati method but couldnt do. Can someone help how can I find the particular solution if it is?
$$4x^2yy'=3x(3y^2+2)+2(3y^2+2)^3$$
2026-04-01 21:30:55.1775079055
Solving Differential Equation $4x^2yy'=3x(3y^2+2)+2(3y^2+2)^3$
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Hint: $$4x^2yy'=3x(3y^2+2)+2(3y^2+2)^3$$ Substitute $u=3y^2+2$
Then you have a Bernoulli's DE. $$\dfrac 23x^2u'=3xu+2u^3$$