newode25.html

restart

with(plots); -1

`:=`(M, `+`(`*`(8, `*`(x)), y, `-`(10)))

`+`(`*`(8, `*`(x)), y, `-`(10))

`:=`(N, `*`(`+`(`*`(9, `*`(x)), `*`(32, `*`(y)), `-`(73)), `/`(1, 9)))

`+`(x, `*`(`/`(32, 9), `*`(y)), `-`(`/`(73, 9)))

`+`(diff(M, y), `-`(diff(N, x)))

0

`:=`(F, `+`(int(N, y), f(x)))

`+`(`*`(x, `*`(y)), `*`(`/`(16, 9), `*`(`^`(y, 2))), `-`(`*`(`/`(73, 9), `*`(y))), f(x))

`:=`(ode, `+`(diff(F, x), `-`(M)) = 0)

`+`(diff(f(x), x), `-`(`*`(8, `*`(x))), 10) = 0

`:=`(sol, dsolve(ode, f(x)))

f(x) = `+`(`*`(4, `*`(`^`(x, 2))), `-`(`*`(10, `*`(x))), _C1)

assign(sol)

F

`+`(`*`(x, `*`(y)), `*`(`/`(16, 9), `*`(`^`(y, 2))), `-`(`*`(`/`(73, 9), `*`(y))), `*`(4, `*`(`^`(x, 2))), `-`(`*`(10, `*`(x))), _C1)

`:=`(F, eval(F, _C1 = 0))

`+`(`*`(x, `*`(y)), `*`(`/`(16, 9), `*`(`^`(y, 2))), `-`(`*`(`/`(73, 9), `*`(y))), `*`(4, `*`(`^`(x, 2))), `-`(`*`(10, `*`(x))))

contourplot(F, x = 0 .. 2, y = 0 .. 4, contours = 10, thickness = 2)

Plot_2d