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Find a power series solution in powers of x . Show the details.

y" + y' + yx^2 =0

y" + y' + yx^2 =0

The equation of a simple harmonic motion is given as d^2x/dt^2 + ω^2x =0. where the symbols have their usual meaning. The dimension of the quantity ω^2 is

a. L^−1

b. M

c. T^−2

d. LT^−2

a. L^−1

b. M

c. T^−2

d. LT^−2

d^2x/dt^2+2 dx/dt+2x = 4cost +2sint x(0) =0; x(0)=3

Solve this IVP Uxx=4xy+e^x ,u(0,y),Ux(0,y)=1

Find the derivative of y=\sin 2x +3\cos 5x

Uxx +Uyy = Q(x,y)

U= C (constant)

this is possions equation ..u are requested to solve it by splitting the problem into two parts.

u=v+w

v----> non-homogeneous equation with homogeneous boundary conditions

w----> homogeneous equation with non homogeneous boundary condition

U= C (constant)

this is possions equation ..u are requested to solve it by splitting the problem into two parts.

u=v+w

v----> non-homogeneous equation with homogeneous boundary conditions

w----> homogeneous equation with non homogeneous boundary condition

(D^4+2D^3-3D^2)Y=3e^2x+4sinx.

The solution of ∂2/∂x∂y (ϕA) at the point (2, -1, 1) of the function ϕ(x,y,z)=xy^2z and A=xzi-xy^2j+xz^2 is ________

A. 4i-2j

B. 5i+6j

C. 3i-2k

D. 3i+3j

A. 4i-2j

B. 5i+6j

C. 3i-2k

D. 3i+3j

Solve the given DE or IVP. First you need to determine what type of DE it is.

y'=sin^2 (3x-3y+1)

y'=sin^2 (3x-3y+1)

Solve d^2u/dx^2 + d^2u/dy^2 =0

Y = 0 , Y = 10 , X = infinity

u (x,y) = x - x ^2 at x = 10

Y = 0 , Y = 10 , X = infinity

u (x,y) = x - x ^2 at x = 10