Determine whether the given relation is an implicit solution to the given differential equation. Assume that the relationship does define y implicitly as a function of x and use implicit differentiation. 12x²y' + (y')³ siny-18 (y')² 3 4x² - 9y 4 sin y + 9xy - x* = 6, y'=- Applying implicit differentiation to the equation gives which 2 y" = 12x²y' + (y) ³ siny-18 (y)² 3 4x - 9y (Type an equation.) -. Therefore, sin y + 9xy - x* = 6 equivalent to a solution to the differential equation.

Advanced Engineering Mathematics
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ISBN:9780470458365
Author:Erwin Kreyszig
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Chapter2: Second-order Linear Odes
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is or is not equivalent and is or is not a solution

Determine whether the given relation is an implicit solution to the given differential equation. Assume that the
relationship does define y implicitly as a function of x and use implicit differentiation.
12x²y' + (y')³ siny-18 (y')²
3
4x² - 9y
4
sin y + 9xy - x* = 6, y'=-
Applying implicit differentiation to the equation gives which
2
y" =
12x²y' + (y) ³ siny-18 (y)²
3
4x - 9y
(Type an equation.)
-. Therefore, sin y + 9xy - x* = 6
equivalent to
a solution to the differential equation.
Transcribed Image Text:Determine whether the given relation is an implicit solution to the given differential equation. Assume that the relationship does define y implicitly as a function of x and use implicit differentiation. 12x²y' + (y')³ siny-18 (y')² 3 4x² - 9y 4 sin y + 9xy - x* = 6, y'=- Applying implicit differentiation to the equation gives which 2 y" = 12x²y' + (y) ³ siny-18 (y)² 3 4x - 9y (Type an equation.) -. Therefore, sin y + 9xy - x* = 6 equivalent to a solution to the differential equation.
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