Lynch Reese
02/21/2024 · Junior High School
\( x y y ^ { \prime } = 2 y ^ { 2 } - x ^ { 2 } \)
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To solve the differential equation \( x y y' = 2y^2 - x^2 \), rearrange it to \( y' = \frac{2y^2}{xy} - \frac{x^2}{xy} \). Use the substitution \( v = \frac{y}{x} \) to simplify and separate variables. Then integrate both sides to find the solution for \( y \) in terms of \( x \).
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