verify that y2 =4a(x+a) is a solution of the differential equation y{1-(dy/dx)2}=2xdy/dx - Maths - Differential Equations

Question

verify that y2 =4a(x+a) is a solution of the
differential equation y{1-(dy/dx)2}=2xdy/dx

Priyanka Kedia · Accepted Answer

Given, y2=4ax+aDifferentiating both side w r t
x, we get,ddxy2=ddx4ax+a⇒2ydydx=ddx4ax+ddx4a2⇒2ydydx=4a+0⇒dydx=2ayNow,L
H S
=y1-dydx2=y1-2ay2           =yy2-4a2y2           =y2-4a2y           =4ax+a-4a24ax+a           =4ax4ax+a           =2x2a4ax+a           =2x2ay           =2xdydx           =R
H S Hence Proved