Question

Find the general solution of the differential equation and check the result by differentiation. dy/dx = x^(3/2)

Answer 1

Given:

`(dy)/(dx)=x^{(3)/(2)}`

To find the general solution:

It can be written as,

`dy=x^{(3)/(2)}dx`

Taking integration on both sides we get,

`\begin{gathered} \int dy=\int x^{(3)/(2)}dx \\ y=\frac{x^{(3)/(2)+1}}{(3)/(2)+1}+c \\ y=\frac{x^{(5)/(2)}}{(5)/(2)}+c \\ y=(2)/(5)x^{(5)/(2)}+c \end{gathered}`

Hence, the general solution is,

`y=(2)/(5)x^{(5)/(2)}+c`

To check the result by differentiation:

Differentiating with respect to x we get,

`\begin{gathered} (dy)/(dx)=(2)/(5)((5)/(2))x^{(5.)/(2)-1}+0 \\ (dy)/(dx)=x^{(3)/(2)} \end{gathered}`

Hence, it is verified.