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If y=X. Sin3x prove that d2y/dx2+9y-6cos3x=0

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If y=X. Sin3x prove that d2y/dx2+9y-6cos3x=0

Posted by Umesh Chaurasia 5 years, 8 months ago

CBSE > Class 12 > Mathematics

1 answers

Rohit Kumar Rai 7 years, 3 months ago

y= x.sin3x ..........................(1) dy/dx = sin3x.dx/dx + x.d(sin3x)/d(3x).d(3x)/dx ( product rule = u.v = u.dv/dx +v.du/dx) dy/dx = sin3x+xcos3x.3 dy/dx = sin3x + 3x.cos3x d^2/dx^2 = cos3x.3 + 3x.( - sin3x.3) +cos3x.3 d^2y/dx^2 = 3cos3x -9xsin3x +3cos3x equation (1) put (xsin3x =y) d^2y/dx^2= -9y+6cos3x d^2y/ dx^2 +9y+6cos3x=0 Answer Hence proved.

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