Differential Equations Answers

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

(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

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

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

Solve the following ODE using the power series method:
(x + 2)y′′ + yx ′ − y = 0

laplace transform to solve the following ode;

4y''+y'-3y=2e^(-5t)

initial conditions y'(0)=0 y(0)=1

solve d^2u/dx^2 +d^2u/dy^2 = 0 which satisfies u (0,y) = u (l,y) = u (x, 0) =0 & u(x,a)= sin nπx/L

Find a power series solution in powers of x-1 of the initial-value problem.
xy''(x) + y'(x) + 2y(x) = 0, y(1) = 2, y'(1) = 4