If y= (1-x2)3/2, show that (1-x2) d2y/dx2 + x dy/dx + 3y = 0 - Maths - Continuity and Differentiability

Question

If y= (1-x2)3/2 , show that
(1-x2) d2y/dx2 + x dy/dx + 3y = 0

Rishabh Mittal · Accepted Answer

Dear Student ,

Please find below the solution to the asked query :

y=1-x232Differentiating both sides wrt x ,dydx=32 1-x232-1 d1-x2dxdydx=32 1-x212 -2xdydx=-3x 1-x212dydx+3x 1-x212=0Multiplying both sides by 1-x21-x2dydx+3x 1-x232=01-x2dydx+3xy=0       Since y=1-x232Differentiating both sides wrt x ,-2x dydx+1-x2d2ydx2+3y+3x dydx=01-x2d2ydx2+x dydx+3y=0Hence Proved 
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If y= (1-x2)3/2 , show that (1-x2) d2y/dx2 + x dy/dx + 3y = 0

If y= (1-x²)^3/₂, show that (1-x²) d²y/dx² + x dy/dx + 3y = 0