If y^3-3ax^2+x^3=0, then prove that (d^2...

If `y^3-3ax^2+x^3=0,` then prove that `(d^2y)/(dx^2)+(2a^2x^2)/(y^5) = 0`

AI Generated Solution

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^3-y=2x , prove that (d^2y)/(dx^2)=-(24 y)/((3y^2-1)^3) .

If x^m y^n=(x+y)^(m+n) , prove that (d^2y)/(dx^2)=0 .

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

If x^m y^n=(x+y)^(m+n) , prove that (d^2y)/(dx^2)=0

If y= A sin x+ B cos x , then prove that (d^2y)/(dx^2)+y=0 .

If y = 5 cos x-3 s in x , prove that (d^2y)/(dx^2)+y=0

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

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

If y=e^(ax) sin bx then prove that (d^2y)/(dx^(2))-2a(dy)/(dx)+(a^(2)+b^(2))y=0 .

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