Please give some hints to solve the differential equation $\frac{dy}{dx}=\frac{1}{x^2+y^2}$ with f(1)=1 in closed form.
Not coming under the usual non homogeneous form or linear form.
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dsolve({diff(y(x), x) = 1/(x^2 + y(x)^2), y(1) = 1}, y(x), implicit);produces $${\frac {-{{ Y}{-3/4}\left(1/2\right)}-{{ Y}{1/4}\left(1/2 \right)}}{{{J}{-3/4}\left(1/2\right)}+{{ J}{1/4}\left(1/2 \right)}}}-{\frac {-{{ Y}{-3/4}\left(1/2, \left( y \left( x \right) \right) ^{2}\right)}y \left( x \right) -{{Y}{1/4}\left( 1/2, \left( y \left( x \right) \right) ^{2}\right)}x}{{{ J}{-3/4 }\left(1/2, \left( y \left( x \right) \right) ^{2}\right)}y \left( x \right) +{{ J}{1/4}\left(1/2, \left( y \left( x \right) \right) ^{2}\right)}x}}=0 .$$ – user64494 Nov 22 '20 at 06:47