A possible solution to dy/dx = 5x^3 is:

1 answer

To solve the differential equation \(\frac{dy}{dx} = 5x^3\), we can integrate both sides with respect to \(x\).

\[ \int dy = \int 5x^3 , dx \]

The left side integrates to:

\[ y = \int 1 , dy = y \]

Now we integrate the right side:

\[ \int 5x^3 , dx = 5 \cdot \frac{x^4}{4} + C = \frac{5}{4}x^4 + C \]

where \(C\) is the constant of integration.

Thus, the general solution to the differential equation is:

\[ y = \frac{5}{4}x^4 + C \]

where \(C\) is an arbitrary constant.