Respuesta :
Answer:
[tex]y(x) = \sqrt[5]{\frac{e^{2x}}{2} + \frac{2047}{2}}[/tex]
Step-by-step explanation:
[tex]\displaystyle\frac{dy}{dx} = \displaystyle\frac{e^{2x}}{5y^4}[/tex]
Cross multiplying, we have,
[tex]5y^4 dy = e^{2x} dx[/tex]
Integrating both sides,
[tex]\int 5y^4 dy = \int e^{2x}dx[/tex]
We obtain,
[tex]y^5 = \frac{e^{2x}}{2} + C[/tex], where C is the constant of integration.
[tex]y(x) = \sqrt[5]{\frac{e^{2x}}{2} + C }[/tex]
We know that y(0) = 4
Putting these value in the above equation, we get C = [tex]\frac{2047}{2}[/tex]
Thus,
[tex]y(x) = \sqrt[5]{\frac{e^{2x}}{2} + \frac{2047}{2}}[/tex]
