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Calculus
Solve the following IVP d^2y/dx^2+ dy/dx -2y = -6sin2x -18cos2x, y(0) =2, y'(0)= 2
Calculus
Find the integrating factor of the differential equation (6xy-3y^2+2y)dx +2(x-y)dy=0 and hence solve it.
Calculus
Solve the following equation by changing the independent variable (1+x^2)^2y"+2x(1+x^2)y'+4y=0.
Calculus
Solve, using the method of variation of parameters d^2y/dx^2-y=2/1+e^x.
Calculus
The normal form of the differential equation y``-4xy``+(4x^2-1)y = -3e^x^2 sin2x is d^2v/dx^2+v =-3sin2x, where v= ye^-x^2. True or false why?
Calculus
The orthogonal trajectories of all the parabolas with vertices at the origin and foci on the x-axis is x^2+2y^2= c^2. True or false ,why?
Calculus
State whether the following statements are true or false. Justify your answer. a) The level curves of x/yz=are hyperbolas. b) 2222)0,0()y,x(yxyxlim+−→does not exist. c) The set }0z,0y,0x|)z,y,x{(<>>is a domain in 3R. d) The work done by the Force )x,y()y,x(F−=in moving a particle along the boundary of the ellipse 36y4x922=−+is 6. e) The function xyze)z,y,x(f=is integrable over ].1,0[]1,0[]1,0
Calculus
Find the directional derivative of f(x,y) = {2 xy/x^2+y^2, (x,y) #(0,0) and 0, (x,y) =(0,0) at (0,0) in the direction of ( i) θ=π/2 (ii) θ= π/4
Calculus
If z= e^x siny ,where x= st^2 and y= s^2 t, find ∂z/∂s and ∂z/∂t.
Calculus
Evaluate ∫∫∫s z^2 dx dy dz where S is the solid region between the spheres ρ =1and ρ = 2 by using spherical coordinates.
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#339914 on Dec 2023
#339914 on Dec 2023