Exact equations
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First determine if the equation is exact. If it is exact, find the general solution, or at least a relation that defines the solutions implicitly:
[cos(x^2 + y) - 3xy^2]y' + 2x cos(x^2 + y) - y^3=0
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Solution Summary
This shows how to find if an equation is exact. The implicit differentiation is provided.
Solution Preview
To find whether it is exact or not we shall rewrite it as:
[cos(x^2 + y) - 3xy^2]dy+[2x cos(x^2 + y) - y^3]dx=0
Then
p(x,y)=2x cos(x^2 + y) - y^3
Q(x,y)=cos(x^2 + y) - 3xy^2
The derivative of P wrt y would ...
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