03:31

Solve:dy/dx=1+x^2+y^2+x^2y^2

08:31

Evaluate Grad e^r^2 or Grad e^(x^2+y^2+z^2)

10:28

Solve the differential equation 2xdy/dx+y(6y^2-x-1)=0

11:33

If r be a unit vector, then show that |rxdr/dt|=|dr/dt|

09:39

Use Cauchy's Mean Value Theorem to evaluate lim x→0 [cos1/2πx/log(1/x)].

03:10

Evaluate ∫∫∫dxdydz from x=0 to x=2,y=0 to y=2,z=0 to z=2.

01:35

What is the degree of the differential equation d^3y/dx^3-3dy/dx-y=0

01:32

Write solution of the differential equation y=px+(p^2-p+2).

01:26

State first shifting theorem

00:38

Evaluate ∫∫∫xydxdydz

02:45

State Convolution theorem

00:51

Write necessary and sufficient condition for the differential equation M(x,y)dx+N(x,y)dy=0 to be exa

00:32

The equation y=px+f(p) is known is Clairaut's equation. (True or False)

01:22

Integrating factor of the given linear differential equation dy/dx+y=1 is e^x (True/false)

01:18

Write sine Fourier Integral formula

02:04

Evaluate ∫∫dxdy from x=0 to x=1,y=0 to y=1.

01:14

Write cosine Fourier integral formula

03:15

Define order of the ordinary differential equation

01:18

Find L-1(s/s^2+16)=......

01:15

Find L(sin5t)=.....

09:18

Prove that J2-J0=2J"0

02:22

Prove that J'0=-J1

40:12

Solve (D^2-DD'-2D'^2+2D+2D')z=e^2x+3y+sin(2x+y)+xy

12:33

Find a complete integral of px+qy+pq=0 by Charpit's Method

20:46

Demorgan's Laws :If A and B are any two sets , then (i) (AUB)'=A'∩B' (ii) (A∩B)'=A'UB'

04:19

If r be a unit vector,then shiw that |rxdr/dt|=|dr/dt|

05:54

The necessary and sufficient condition for the vector a(t) to have constant direction is axda/dt=0

11:27

Solve (D^2-DD'-6D'^2)z=xy

05:38

Evaluate ∫z^2+6z-1/(z-4)dz over the closed curve C ,where C is the circle|z|=5.

14:47

Prove that the condition that xcodα+ysinα=p should touch the curve x^my^n=a^m+n is p^m+nm^mn^n=(m+n)

03:28

Find yn if f(x)=/x-1

09:07

Evaluate d^2/dx^2[r dr/dt d^2r/dt^2]

08:55

Sove :(D^2-2D+5)y=10sinx.

03:41

Separate into real and imaginary parts of Cosh(α+iβ)

06:59

Separate into real and imaginary parts of cot(α+iβ) .

04:14

Separate into real and imaginary parts of sinh(α+iβ).

02:17

Show that cos(α+iβ)=cosαcoshβ-isinαsinhβ

02:38

Show that sin(α+iβ)=sincosh

15:17

Solve : d^2y/dx^2-4xdy/dx+(4x^2-1)y=-3e^x^2sin2x.

39:57

Expand f(z)=1/(z+1)(z+3) in a Laurent's series valid for the regions (i) 1 less than|z| leas rhan 3

19:39

Trace the curve y(1-x^2)=x^2

20:07

Sum to n terms of the series cosx+cos3x+cos5x+.....

07:37

Prove that sinh(α+β)=sinhα.coshβ+coshα.sinhβ

05:08

If |2z-1|=|z-2|, prove that the point z=x+iy lies on the circle x^2+y^2=1.

12:26

Find all the roots of the equation x^5-1=0.

20:15

Find the position and nature of the double points on the curve:x^3-4x^2+4x-2y^2=0.

13:22

Find the radius of curvature at any point of the curve x=a(θ-sinθ),y=a(1-cosθ).

05:45

Show that the function f(z)=x-iy is not analytic at any point.

04:53

If y=cosnnx+sinnx,then prove that d^2y/dx^2+n^2y=0.

03:07

If z=x^3+y^3/x-y then show that x∂z/∂x+y∂z/ ∂y=2z.

02:30

Separate real and imaginary parts of e^α+iβ.

14:31

Solve:d^2y/dx^2-y=e^2x(sinx+x+1)

02:30

10 लड़कियों और 20 लड़कों की एक कक्षा में जया का स्थान लड़कियों में चौथा और कक्षा में 18 वां है ।जया

04:49

find the modulus and amplitude of the complex number 1+i√3

04:07

Prove that sin3θ=3sinθ-4sin^3θ

04:09

Find the asymptote (s) that are parallel to the x-axis of the curve x^2y^2-9x^2=1.

25:29

∫e^z/z^2(z+1)^3dz,C: |z|=2

03:18

Find the radius of curvature at (1,0) on the curve y=x^2+1.

07:04

Solve:y'+ytanx=sin2x,y(0)=1.

18:25

Solve:d^2y/dx^2+2xdy/dx+(x^2+5)y=xe^-1/2x^2