solution to 1st order non linear ODE I have to solve the O.D.E 

$$x\left(\frac{\mathrm dy}{\mathrm dx}\right)-25=y^2$$ 


My attempt at a solution so far is: 
$$x\left(\frac{\mathrm dy}{\mathrm dx}\right)=y^2+25$$
$$\frac{\mathrm dy}{(y^2+25)}=\frac{\mathrm dx}{x}$$
let $u:=y/5$
$$\implies \frac{\mathrm du}{5(u^2-1)}=\frac{\mathrm dx}{x}$$
Integrating both sides then yields 
$$(1/5)\arctan(y/5)+C=\ln(x)+C \implies \arctan(y/5)=5\ln(x)+C$$
$$ \implies \arctan(y/5)=5\ln(x)+C \implies y/5=\tan(5\ln(x)+C)$$
$$\implies y/5=\tan(5\ln(x)+C)$$

$$y=5\tan(5\ln(x)+C)$$

if someone could please tell me if this is correct or not that would be great, and if it is incorrect any hints,tips or tricks would be hugely appreciated :)

Your solution $y(x)=5 \tan(5 \ln x+C)$ is correct !
