1.

Find the general solution of each of the following differential equations: `(1)/(x)cos^(2)y dy +(1)/(y)cos^(2)xdx=0`

Answer» Correct Answer - `2(x^(2)+y^(2))+2xsin2x+2y sin2y+cos2x+cos2y=C`
`ycos^(2)y dy +xcos^(2)x dx =0 rArr y(2cos^(2)y)dy +x(2cos^(2)x)dx=0`
`rArr y(1+cos2y)dy+x(1+cos2x)dx=0`
`rArr int y dy +int y cos 2y dy +int x dx +int x cos2x dx = C`
`rArr (x^(2))/(2)+(y^(2))/(2)+int underset(I)(y)underset(II)(cos 2y)dy+int underset(I)(x)underset(II)(cos 2x)dx =C.`


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