(i) If y=asin(log x) then prove that x^(...

(i) If `y=asin(log x)` then prove that `x^(2)(d^2y)/(dx^2)+x(dy)/(dx)+y=0`.
(ii) If `y=acos(log_(e)x)+bsin(log_(e)x)`, then prove that `x^2(d^2y)/(dx^2)+x*dy/dx+y=0`.

Continuity and Differentiability
NAGEEN PRAKASHAN ENGLISH|Exercise Exercies 5m|18 Videos
Continuity and Differentiability
NAGEEN PRAKASHAN ENGLISH|Exercise Exercies 5n|10 Videos
Continuity and Differentiability
NAGEEN PRAKASHAN ENGLISH|Exercise Exercies 5k|12 Videos
APPLICATIONS OF INTEGRALS
NAGEEN PRAKASHAN ENGLISH|Exercise Miscellaneous Exercise|19 Videos
DETERMINANTS
NAGEEN PRAKASHAN ENGLISH|Exercise Miscellaneous Exercise|19 Videos

Similar Questions

Explore conceptually related problems

If y="sin"(logx), then prove that (x^2d^2y)/(dx^2)+x(dy)/(dx)+y=0

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

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

If y=acos(logx)+bsin(logx), prove that x^2(d^2y)/(dx^2)+\ x(dy)/(dx)+y=0

If y=Acos(logx)+B sin(logx) then prove that x^(2)(d^(2)y)/(dx^(2))+x(dy)/(dx)+y=0 .

If y=Acos(logx)+\ Bsin(logx) , prove that x^2\ (d^2y)/(dx^2)+x(dy)/(dx)+y=0 .

If x=tan(1/a log y) , prove that (1+x^2) (d^2y)/(dx^2)+(2x-a) (dy)/(dx)=0

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

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

If y=log\ [x+sqrt(x^2+1)] , prove that (x^2+1)(d^2\ y)/(dx^2)+x(dy)/(dx)=0

Find the 2nd derivative if x^3 log x with respect to x.
Text Solution
|
If y=tan^(-1)x^3 then find (d^2y)/(dx^(2)).
Text Solution
|
Find the 2nd dervative of e^(ax+b) with respect to x.
Text Solution
|
If y=x+cotx then prove that sin^2x(d^2y)/(dx^2)-2y+2x=0.
Text Solution
|
If y=log(sinx) , prove that (d^3y)/(dx^3)=2cosx cos e c^3x .
Text Solution
|
If y=Acosn x+Bsinn x ,s howt h a t (d^2y)/(dx^2)+n^2y=0
Text Solution
|
(i) If y=asin(log x) then prove that x^(2)*(d^2y)/(dx^2)+x(dy)/(dx)+y=...
Text Solution
|
If y=(sin^(-1)x)^2 then prove that (1-x^(2))(d^2y)/(dx^2)-x(dy)/(dx)-2...
Text Solution
|
If y=sin(sinx) , prove that (d^2y)/(dx^2)+tanxdot(dy)/(dx)+y\ cos^2x=0...
Text Solution
|
IF y=e^(tan^(-1)x) then prove that : (1+x^(2))(d^2y)/(dx^2)+(2x-1)(d...
Text Solution
|
If y^3-3ax^2+x^3=0, then prove that (d^2y)/(dx^2)+(2a^2x^2)/(y^5) = 0
Text Solution
|
If y=(t a n^(-1)\ x^2) , show that (x^2+1)^2(d^2\ y)/(dx^2)+2x(x^2+1)(...
Text Solution
|
If y=e^tanx then prove that: cos^2x(d^2y)/(dx^2)-(1+sin2x)(dy)/dx=0
Text Solution
|
If y=A e^(-k t)cos(p t+c), then prove that (d^2y)/(dt^2)+2k(dy)/(dx)+n...
Text Solution
|
If x=at^2,y=2 at then find (d^2y)/(dx^2).
Text Solution
|
If x=a(t-sint), y=a(1-cost) then find (d^2y)/(dx^2).
Text Solution
|
If x=sint and y=sinp t , prove that (1-x^2)(d^2y)/(dx^2)-x(dy)/(dx)+p^...
Text Solution
|
If y=(sin^(-1)x)^2+(cos^(-1)x)^2, then prove that (1-x^2)y2-xy(1)-4=0.
Text Solution
|