I have solved for $z(w,x,y)$ in a differential equation:
$$ 3\frac{\partial z}{\partial y} = 2(z-1) + (1-wy^2 )x $$
And I obtained the general solution: $z = f(w,x,y)$
Now putting in $x=0$, we have $z_0 = f(w,0,y) = g(w,y)$
Then I am trying to solve for $x^*(w,y)$ this final equation and contour plot it:
$$ f(w,x^*,y) = 2.7 \times g(w,y)$$
I've managed to obtain $f(w,x,y)$ and $g(w,y)$, which should be the hardest part. Then I'm not sure why the last part of the code is not working, as the last part should be rather straightforward.
pde1 = 3*D[z[w, x, y], y] == 2 (z[w, x, y] - 1) + (1 - y^2 w) x
soln1 = DSolve[pde1, z[w, x, y], {w, x, y}]
soln5 = soln1 /. {x -> 0}
eqn1 = soln5 == 2.7*soln1
ContourPlot[
x /. Solve[eqn1, x, Method -> Reduce], {w, 1, 5}, {y, 1, 5},
PlotRange -> All]
DSolve[]
doesn't return solutions with that init cond.! $\endgroup$