solve the differential equation `dy/dx = 15x^4y^4` with the condition that y(0)=5 the solution to the equation is y=

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This equation can be solved by separation of the variables:

`dy/y^4 = 15x^4dx`

Integrating both sides, get

`-1/(3y^3) = 15 x^5/5 + C`

Since y(0) = 5, `-1/(3*5^3) = C`  and `C = -1/375`

 `-1/(3y^3) =3x^5-1/375 `

`-1/y^3 =9x^5 - 1/125`

`y = -1/root(3)(9x^5 - 1/125)`

 

 

 

 

 

 

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