## Related questions with answers

Question

Show that

$d f=y\left(1+x-x^2\right) d x+x(x+1) d y$

is not an exact differential. Find the differential equation that a function $g(x)$ must satisfy if $d \phi=g(x) d f$ is to be an exact differential. Verify that $g(x)=e^{-x}$ is a solution of this equation and deduce the form of $\phi(x, y)$.

Solution

VerifiedAnswered 2 years ago

Answered 2 years ago

Step 1

1 of 3Differential equation is:

df= Adx+ Bdy

To check whether the equation is exact differential equation or not :

$\dfrac{\partial A}{\partial y}= \dfrac{\partial B}{\partial x}$

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