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Popular Calculus >

y^'=a-by^2

Solution

y^{^{'}} = a - b y^{2}

Solution

y = - \frac{a e ^{2 a b t + 2 c_{1} a b}}{b ( 1 - e ^{2 a b (t + c_{1})} )} - \frac{a}{b ( 1 - e ^{2 a b (t + c_{1})} )}

Solution steps

y^{'} (t) = a - b y^{2}

Solve separable ODE:

y = - \frac{a e ^{2 a b t + 2 c_{1} a b}}{b ( 1 - e ^{2 a b (t + c_{1})} )} - \frac{a}{b ( 1 - e ^{2 a b (t + c_{1})} )}

y = - \frac{a e ^{2 a b t + 2 c_{1} a b}}{b ( 1 - e ^{2 a b (t + c_{1})} )} - \frac{a}{b ( 1 - e ^{2 a b (t + c_{1})} )}

Graph

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Frequently Asked Questions (FAQ)

What is the solution for y^'=a-by^2 ?
The solution for y^'=a-by^2 is