Find an explicit particular sol'n of the initial value problem x(dx/dy)-y=2x^2 y.

Bernard Boyer 2022-07-26 Answered

Find an explicit particular sol'n of the initial value problem

x * (d x / d y) - y = 2 x^{2} * y

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Jamarion Roth

Answered 2022-07-27 Author has 13 answers

x * (d x / d y) - y = 2 x^{2} * y

x y^{'} = y (1 + 2 x^{2})

y^{'} / y = (1 + 2 x^{2}) / x

this is a separable diff. eqn.

\frac{d y}{y} = \frac{(1 + 2 x^{2})}{x} d x

\int \frac{d y}{y} d y = \int \frac{(1 + 2 x^{2})}{x} d x = \int (\frac{1}{x} + 2 x) d x

\ln (y) = \ln (x) + x^{2} + c

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