Differential Equations Answers

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

(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

Verify that the equations
Z=√(2x+a) + √(2y+ b). And
Z^2 + m = 2 ( 1+ £^-1) (x + £y)
Are both the complete integrals of the PDE z = 1/p +1/q . Also show that the complete integral of second equation is the envelope of the one parameter sub system obtained by taking b = -a/ £ - m/ 1+£ in the solution first