Solve $(8$x$+7$y$)$dx$+(7$x$+35$y$4)$dy$=0$

Follow the step$-$by$-$step instruction below to learn to solve the exact differential equation.

Suppose P$($x$,$y$)=(8$x$+7$y$)$ and Q$($x$,$y$)=(7$x$+35$y$4)$

P$($x$,$y$)$dx$+$Q$($x$,$y$)$dy$=0$ is exact on R if

Px$($x$,$y$)=$Qx$($x$,$y$)$

Py$($x$,$y$)=$Qx$($x$,$y$)$

Py$($x$,$y$)=$Qy$($x$,$y$)$

Px$($x$,$y$)=$Qy$($x$,$y$)$

Make sure you verify the statement.

Therefore, the Exactness Theorem implies that there's a function F such that Fx$($x$,$y$)=$P$($x$,$y$)$ and Fy$=$Q$($x$,$y$).$

Thus F$($x$,$y$)=$P$($x$,$y$)$d $?$ x y

Meaning we integrate $8$x$+7$y with respect to x to obtain our first glimpse of the potential function.

F$($x$,$y$)=4$x$2+7$xy$+$ Select an answer C h$($x$)$ h$($y$)$

We now differentitate F$($x$,$y$)=4$x$2+7$xy$+$h$($y$)$ with respect to $?$ x y

to obtain $.$