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Popular Calculus >

a-by^2=(dy)/(dx)

Solution

a - b y^{2} = \frac{d y}{d x}

Solution

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

Solution steps

a - b y^{2} = \frac{d y}{d x}

Solve separable ODE:

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

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

Graph

Popular Examples

slope of (3.9)(-5.3)

integral of 1/((1+x^2)^{5/2)}

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derivative of f(x)=5^{-x}

Frequently Asked Questions (FAQ)

What is the solution for a-by^2=(dy)/(dx) ?
The solution for a-by^2=(dy)/(dx) is