Answer to Question #316642 in Differential Equations for Tobias Felix

Question #316642

Integrating factors found by inspection

y(x^2 y^2 − 1)dx + x(x^2 y^2 + 1)dy = 0


1
Expert's answer
2022-03-24T18:47:56-0400

"y(x^2 + y^2 \u2212 1)dx + x(x^2 + y^2 + 1)dy = 0\\\\\n(x^2y + y^3 \u2212 y)dx + (x^3 + xy^2 + x)dy = 0\\\\\nx^2ydx + y^3dx \u2212 ydx + x^3dy + xy^2dy + xdy = 0\\\\\nx^2(ydx+xdy)+y^2(ydx+xdy)+xdy-ydx=0\\\\\n\\left[(ydx+xdy)(x^2+y^2)+xdy-ydx =0\\right]\\frac{1}{x^2+y^2}\\\\\nydx+xdy+ \\frac{xdy-ydx}{x^2+y^2}=0\\\\\nd(xy)+d(\\arctan (\\tfrac{y}{x}))=0\\\\\n\\int d(xy)+ \\int d(\\arctan (\\tfrac{y}{x}))= \\int 0\\\\\nxy+ \\arctan \\tfrac{y}{x}= c"


Need a fast expert's response?

Submit order

and get a quick answer at the best price

for any assignment or question with DETAILED EXPLANATIONS!

Comments

No comments. Be the first!

Leave a comment

LATEST TUTORIALS
New on Blog
APPROVED BY CLIENTS