First Test Caxom:

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Consider the following differential equation.

$(x-y^7{y}^{2}sin(x))dx=(7x{y}^{6}2ycos(x))dy$

Let $M=y^7-y^{2}sin(x)-x$ and $N=7x{y}^{6}2ycos(x).$ Find the following partial derivatives.

$M_y=$

$N_x=$

Is the given differential equation exact?

Yes

No

Let $\frac{\text{d}\text{e}\text{l}\text{f}}{\text{d}\text{e}\text{l}\text{x}}=y^7-y^{2}sin(x)-x.$ Integrate this partial derivative with respect to $x,$ letting $A(y)$ be an unknown function in $y.$

$(x,y)=M(y)$

Find the derivative of $h(y).$

$A^{\text{'}\text{'}}(v)=$

Find the general solution of the given differential equation. $($If it is not exact, enter NOT.$)$

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Thenting virew

marestity mits.

$5$ewith