# Solve the differential equation dy/dx=15x^4y^4 with the given condition that y(0)=5 .

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

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

integrating both sides:

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

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

`y(0)=5`

`-1/375=c`

`y=5/root(3)(1-1125x^5) `

Please in above answer , here is a correction after calculation of

`c=(-1)/375`

`y^(-3)=(-3){3x^5-1/375}`

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

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

Given

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

`` In this problems ,variable are separable,Thus

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

Integrating both side ,we have

`int(dy/y^4)=int(15x^4dx)+c`

`y^(-4+1)/(-3)=15x^(4+1)/5+c`

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

given x=0 ,y=5

`-(1/3)5^(-3)=c`

`c=-1/375`

`y=(-3){3x^5-1/375)`

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