How do I attempt to write this (d/dx(5y^3​+3y^2)=7y*​(1+y)) nonlinear differential equation and start solving it on MATLAB?

Apologies if this may seem basic. I'm not sure where to go to find information on how to solve this. For simplicity I've written it down as d/dx(5y^3+3y^2)=7y*(1+y). The original equation is very similar but with a lot more parameters.

How do I attempt to write this and start solving it on MATLAB? Any advice is appreciated

[Vladimir Sovkov]

syms y
diff(5*y^3+3*y^2)

ans =

15*y^2 + 6*y

The equation is equivalent to . Hence, besides the obvious y=0, . So

syms y
int((15*y+6)/7/(1+y))

ans =

(15*y)/7 - (9*log(y + 1))/7

[HFMatlab]

Thank you @Vladimir Sovkov. Say that the inital condition is y=0, and I want to solve this between an interval of x=1:1:10; can I still follow this method?

[Vladimir Sovkov]

The complementary solution in this example is with an arbitrary C. With it gives . Consequently, the solution with the boundary condition is the one with , i.e. . It is not easy to rewrite it in a form . The other solution also fulfils your boundary condition.