Differential Equations Answers

Solve the PDE
1.(D^2+D-1)z=4e^(x+y) cos(x+y)

Verified that the equations
1.z=root(
2x+a)+root(2y+b) and
2.z^2+meu=2(1+lemda^-1)(x+lemda y)

are both complete integrals of the PDE z=1/p+1/q.Also show that the complete integral (2)is the envelope of the one parameter sub-system obtained by taking b=-a/lemda-meu/(1+lemda) in the solution (1)

If d2x/dt2+g(x-a)/b=0, (a, b, gbeing positive constants) and x = a′ and dx/dt=0 when t=0, show that x=a+(a'-a)cos {g underoot t/b}

Solve the partial differential equation

(D+D'-1)(D+2D'-3)z=4+3x+6y

Solve the PDE
1.(D^2+D-1)z=4e^(x+y) cos(x+y)
2.(D+D'-1)(D+2D'-3)z=4+3x+6y

A tightly stretched string with fixed end points x=0 and x=l is initially in a position given by y=y0sin^3(πx/l).It is released from rest from the initial position. Find the displacement y(x,t).

Find the surface which is orthogonal to the one parameter system
z=c xy(x^2+y^2) and which passes through the hyperbola
X^2-y^2=a,z=0.

Find the general integral of the equation
(Xyy)p+(y-x-z)q=z
and particular solution through the circle
Z=1,x^2+y^2=1.

1.Find the differential equations of the space curve in which the two families of surfaces u=x^2-y^2=c1 andv=y^2-z^2=c2 intersect.
2. Find value of n for which the equation (n-1)^2 u_xx-y^2n u_yy=ny^(2n-1) u_y is parabolic or hyperbolic.