34. The solution of the p.d.e.?
ptanx + qtany= tanz
Answers
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Answer:
Simplifying
ptanx + qtany = tanz
Solving
anptx + anqty = antz
Solving for variable 'a'.
Move all terms containing a to the left, all other terms to the right.
Add '-1antz' to each side of the equation.
anptx + anqty + -1antz = antz + -1antz
Combine like terms: antz + -1antz = 0
anptx + anqty + -1antz = 0
Factor out the Greatest Common Factor (GCF), 'ant'.
ant(px + qy + -1z) = 0
Subproblem 1
Set the factor 'ant' equal to zero and attempt to solve:
Simplifying
ant = 0
Solving
ant = 0
Move all terms containing a to the left, all other terms to the right.
Simplifying
ant = 0
The solution to this equation could not be determined.
This subproblem is being ignored because a solution could not be determined.
Subproblem 2
Set the factor '(px + qy + -1z)' equal to zero and attempt to solve:
Simplifying
px + qy + -1z = 0
Solving
px + qy + -1z = 0
Move all terms containing a to the left, all other terms to the right.
Add '-1px' to each side of the equation.
px + qy + -1px + -1z = 0 + -1px
Reorder the terms:
px + -1px + qy + -1z = 0 + -1px
Combine like terms: px + -1px = 0
0 + qy + -1z = 0 + -1px
qy + -1z = 0 + -1px
Remove the zero:
qy + -1z = -1px
Add '-1qy' to each side of the equation.
qy + -1qy + -1z = -1px + -1qy
Combine like terms: qy + -1qy = 0
0 + -1z = -1px + -1qy
-1z = -1px + -1qy
Add 'z' to each side of the equation.
-1z + z = -1px + -1qy + z
Combine like terms: -1z + z = 0
0 = -1px + -1qy + z
Simplifying
0 = -1px + -1qy + z
The solution to this equation could not be determined.
This subproblem is being ignored because a solution could not be determined.
The solution to this equation could not be determined.
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