Class 12

Math

Calculus

Differential Equations

Find the general solution of the differential equations $sec_{2}xtanydx+sec_{2}ytanxdy=0$

$sec_{2}xtanydx=−sec_{2}ytanxdy$

$tanxsec_{2}x dx=−tanxsec_{2}x dx$

Let $tanx=tandtany=h$

Then,$sec_{2}xdx=dtandsec_{2}ydy=dh$

Puting these values in our differential equation,

$tdt =−hdh $

Integrating both sides,

$∫tdt =∫−hdh $

$⇒ln(t)=−ln(h)+c$

$⇒ln(t)+ln(h)=c$

$⇒ln(th)=c$

$⇒ln(tanxtany)=c$

$⇒tanxtany=e_{c}$

$⇒tanxtany=C$

, which is the required solution.