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WHAT IS THE DIFFERENTIAL EQUATION for tan(x^2+y^2)dy=xdx+ydy.?
WHAT IS THE DIFFERENTIAL EQUATION for tan(x^2+y^2)dy=xdx+ydy, does any body know?
what are the steps? I used the intergrating factor for the group term xdx+ydy, IF 1/(x^2+y^2). but my answer does not make sense. Anyone, please.
1 Answer
- ?Lv 67 years agoFavorite Answer
What an ugly question but easier than you think as
tan[(x^2) + (y^2)] dy = x dx + y dy
tan[(x^2) + (y^2)] = x dx/dy + y
u = (x^2) + (y^2);
du/dy = 2x * dx/dy + 2y
1/2 * du/dy = x dx/dy + y
tan(u) = 1/2 * du/dy
1 = 1/2 * cot(u) * du/dy
2 dy = cot(u) du
2y + C = ln|sin(u)|
2y + C = ln|sin((x^2) + (y^2))|
C = ln|sin((x^2) + (y^2))| - 2y
