DIFFERENTIAL EQUATIONS — Maths STD 12 Science — Question

$\frac{\text{dy}}{\text{dx}}=\text{x}^5+\text{x}^2-\frac{2}{\text{x}},\text{x}\ne0$

$\Rightarrow\text{dy}=\Big(\text{x}^5+\text{x}^2-\frac{2}{\text{x}}\Big)\text{dx}$

Intergrating both sides, we get

$\Rightarrow\int\text{dy}=\int\Big(\text{x}^5+\text{x}^2-\frac{2}{\text{x}}\Big)\text{dx}$

$\Rightarrow\text{y}=\frac{\text{x}^6}{6}+\frac{\text{x}^3}{3}-2\log|\text{x}|+\text{C}$

Clearly, $\Rightarrow\text{y}=\frac{\text{x}^6}{6}+\frac{\text{x}^3}{3}-2\log|\text{x}|+\text{C}$ is defined for all $\text{x}\in\text{R}$ except x = 0

Hence,  $\Rightarrow\text{y}=\frac{\text{x}^6}{6}+\frac{\text{x}^3}{3}-2\log|\text{x}|+\text{C}$, where $\text{x}\in\text{R}-\{0\},$ is the solution o the given differential equation.