" 11."(d^(2)y)/(dx^(2))=x+sin x," दिया है "y=0,(dy)/(dx)=-1" यदि "x=0

(d^(2)y)/(dx^(2))=x^(2)sin x, givenatx =0 if y=0,(dy)/(dx)=1

(d^(2)y)/(dx^(2))=(1)/(1+x^(2)) whenx =0,y=0 and (dy)/(dx)=0

x(d^(2)y)/(dx^(2))+(dy)/(dx)+x=0

If y= sin (sin x) then show that, (d^(2)y)/(dx^(2)) + (tan x) (dy)/(dx) + y cos^(2)x = 0

If y= e^(tan x) then show that, (cos^(2)x) (d^(2)y)/(dx^(2))- (1+ sin 2x) (dy)/(dx)=0

[" The differential equation of the family of curves "],[y=c_(1)x^(3)+(c_(2))/(x)" where "c_(1)" and "c_(2)" are arbitrary "],[" constants,is "],[" O "x^(2)(d^(2)y)/(dx^(2))-x(dy)/(dx)-3y=0],[" (x) "(d^(2)y)/(dx^(2))+x(dy)/(dx)+3y=0],[" (x) "(d^(2)y)/(dx^(2))+x(dy)/(dx)-3y=0],[" (x) "(d^(2)y)/(dx^(2))-x(dy)/(dx)+3y=0]

If y=x^(x) , prove that (d^(2)y)/(dx^(2))-(1)/(y)((dy)/(dx))^(2)-(y)/(x)=0 .

If y=sin(sin x), prove that (d^(2)y)/(dx^(2))+tan x(dy)/(dx)+y cos^(2)x=0

If y =sin (sin x) and (d^(2)y)/(dx^(2))+(dy)/(dx) tan x + f(x) = 0, then find f(x).

If y =sin (sin x) and (d^(2)y)/(dx^(2))+(dy)/(dx) tan x + f(x) = 0, then find f(x).