Question

the general solution of dy/dx = x^3 is​

Answer 1

Answer:

Step-by-step explanation:

We have,

$\rm{\dfrac{dy}{dx}={x}^{3}}$

This could be solved by variable separation method,

$\rm{dy={x}^{3}\,dx}$

Integrating both sides,

$\displaystyle\rm{\int\,dy=\int{x}^{3}\,dx}$

$\displaystyle\rm{\implies\,y=\dfrac{{x}^{3+1}}{3+1}+c}$

$\displaystyle\rm{\implies\,y=\dfrac{{x}^{4}}{4}+c}$

$\displaystyle\rm{\implies\,4y={x}^{4}+4c}$

Since c is an arbitrary constant, so, put 4c = C

$\displaystyle\rm{\implies\,4y={x}^{4}+C}$