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solve DE xdy-ydx=(x^2+y^2)dx?
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Verified answer
x dy − y dx = (x² + y²) dx
(x dy − y dx) / x² = (1 + y²/x²) dx
d (y/x) = (1 + y²/x²) dx
Let u = y/x
du = (1 + u²) dx
du/(1+u²) = dx
∫ du/(1+u²) = ∫ dx
tan⁻¹(u) = x + C
u = tan(x+C)
y/x = tan(x+C)
y = x tan(x+C)