Solve the following differential equation: `(dy)/(dx)=x^5+x^2-2/x ,\ x!=0`

Explanation

`frac{d y}{d x}=x^{5}+x^{2}-frac{2}{x} `

`
Rightarrow d y=(x^{5}+x^{2}-frac{2}{x}) d x`



By Integrating , we obtain

`
Rightarrow int d y=int(x^{5}+x^{2}-frac{2}{x}) `

`d x Rightarrow y=frac{x^{6}}{6}+frac{x^{3}}{3}-2 log |x|+C `

hence ,` y=frac{x^{6}}{6}+frac{x^{3}}{3}-2 log |x|+C`