xydx+(x+1)dy=0 find special solutions
Answers
Answer:
Simplifying
(xy) * dx + (x + 1) * dy = 0
Multiply xy * dx
dx2y + (x + 1) * dy = 0
Reorder the terms:
dx2y + (1 + x) * dy = 0
Reorder the terms for easier multiplication:
dx2y + dy(1 + x) = 0
dx2y + (1 * dy + x * dy) = 0
Reorder the terms:
dx2y + (dxy + 1dy) = 0
dx2y + (dxy + 1dy) = 0
Reorder the terms:
dxy + dx2y + 1dy = 0
Solving
dxy + dx2y + 1dy = 0
Solving for variable 'd'.
Move all terms containing d to the left, all other terms to the right.
Factor out the Greatest Common Factor (GCF), 'dy'.
dy(x + x2 + 1) = 0
Subproblem 1
Set the factor 'dy' equal to zero and attempt to solve:
Simplifying
dy = 0
Solving
dy = 0
Move all terms containing d to the left, all other terms to the right.
Simplifying
dy = 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 '(x + x2 + 1)' equal to zero and attempt to solve:
Simplifying
x + x2 + 1 = 0
Reorder the terms:
1 + x + x2 = 0
Solving
1 + x + x2 = 0
Move all terms containing d to the left, all other terms to the right.
Add '-1' to each side of the equation.
1 + x + -1 + x2 = 0 + -1
Reorder the terms:
1 + -1 + x + x2 = 0 + -1
Combine like terms: 1 + -1 = 0
0 + x + x2 = 0 + -1
x + x2 = 0 + -1
Combine like terms: 0 + -1 = -1
x + x2 = -1
Add '-1x' to each side of the equation.
x + -1x + x2 = -1 + -1x
Combine like terms: x + -1x = 0
0 + x2 = -1 + -1x
x2 = -1 + -1x
Add '-1x2' to each side of the equation.
x2 + -1x2 = -1 + -1x + -1x2
Combine like terms: x2 + -1x2 = 0
0 = -1 + -1x + -1x2
Simplifying
0 = -1 + -1x + -1x2
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
Step-by-step explanation:
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