Course Teacher: Dr.T.N. Shanmugam
E-Mail: shan@annauniv.edu
Last date for submission: 22nd August 2008
1. Obtain a PDE satisfied by all spheres whose centers lie on the z-axis.
2. Determine the PDE satisfied by all right circular cones whose axes coincide with the z-axis.
3. Find the PDE by eliminating the arbitrary function from
z = xy + g(x2 - y2)
4. Classify all the solutions of a PDE.
5. Find the general solution of the PDE
z(p - q) = z^2 + (x + y)^2.
6. Find the completer integral of the PDE
zpq = p + q.
7. Solve the PDE
(p^2)(q^2) + (x^2)(y^2) = (x^2)(q^2)(x^2 + y^2)
8. Solve using the transformation X = x^2; Y = y^2 the PDE
4xyz = pq + 2p(x^2)y + 2qx(y^2)
9. Find the complete integral of the PDE
z^2 = pqxy
10. Find a complete integral of the PDE
(p^2)x + qy - z = 0
and hence derive the equation of an integral surface which contains the
line y = 1; x + z = 0
2. Determine the PDE satisfied by all right circular cones whose axes coincide with the z-axis.
3. Find the PDE by eliminating the arbitrary function from
z = xy + g(x2 - y2)
4. Classify all the solutions of a PDE.
5. Find the general solution of the PDE
z(p - q) = z^2 + (x + y)^2.
6. Find the completer integral of the PDE
zpq = p + q.
7. Solve the PDE
(p^2)(q^2) + (x^2)(y^2) = (x^2)(q^2)(x^2 + y^2)
8. Solve using the transformation X = x^2; Y = y^2 the PDE
4xyz = pq + 2p(x^2)y + 2qx(y^2)
9. Find the complete integral of the PDE
z^2 = pqxy
10. Find a complete integral of the PDE
(p^2)x + qy - z = 0
and hence derive the equation of an integral surface which contains the
line y = 1; x + z = 0
2 comments:
it wil be nice if u post wit d answers..
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