(Solved): #30 please and explain when possible. The method outlined in Problem 25 can be used for any homogen ...

The method outlined in Problem 25 can be used for any homogencous equation. That is, the substitution $$y=xv(x)$$ transforms a homogeneous equation into a separable equation. The latter equation can be direct integration, and then replacing $$v$$ by $$y/x$$ gives the solutic $$?$$ original equation. In each of Problems 26 through 31 : a. Show that the given equation is homogeneous. b. Solve the differential equation. c. Draw a direction field and some intorgral curves. Are they symmetric with respect to the origin? 26. $$\frac{dy}{dx}=\frac{x^2+xy+y^2}{x^2}$$ 27. $$\frac{dy}{dx}=\frac{x^2+3y^2}{2xy}$$ 28. $$G\frac{dy}{dz}=\frac{4y?3x}{2z?y}$$ 29. $$\frac{dy}{dx}=?\frac{4x+3y}{2x+y}$$ 30. $$\frac{dy}{4x}=\frac{x^3?3y^2}{2xy}$$ $$?\mathbf{n}\frac{dy}{}?\frac{3r^2?c^2}{}$$