Differential Equations Answers

NOU134362937: The order of differential equation
d^2y/dx^2+2 dy/dx d^3y/dx^3 + x=0 is __________
a. 1
b. 3
c. 4
d. 2

Find the value of
m
so that the function
y=e^mx
is a solution of the differential equation
y′+2y=0

a=0
b=3
c=1
d=2

(D²+3DD'+2D') = cos (x+3y)

Show that the function z = Iog (x2 + y2) satisfies the equation d2z/dx2+ d2z/d y2 = 0

d^2y/dx^2+3(dy/dx)+ 2y=1+3x+x^2

(D²+3DD'+2D'²)z=12xy

(x+2)y"+xy'-y=0

d2y/dx2+3dy/dx-10y=3x2

Obtain a solution of the wave equation
∂^2u(x,t)/∂t^2=16(∂^2u(x,t)/∂x^2)

for 0≤ x ≤ π and t > ,0 and the following boundary and initial conditions:
u(0,t)=u(π,t)=0,
u(x,0)=x(π-x) and ∂u(x,0)/∂t=0

Reduce the following PDE to a set of three ODEs by the method of separation of
variables (1/r)(∂/∂r)(r(∂V/∂r)+(1/r^2)(∂^2V/∂θ^2)+(∂^2V/∂z^2)+(k^2)V=0