Differential Equations
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I thank. but the Riccati equation y =? special solution y = y 1 + 1 / u do not solve the equation
Riccati EQUATION
p (x), r (x) and g (x) integrable function and r (x) ≠ 0, including
y '= p (x) y + r (x) y2 + g (x)
Type in the differential equation 'Riccati Differential Equation' is called.
If r (x) = 0, linear differential equations,
g (x) = 0 takes the form of the Bernoulli equation.
As a general solution y = y 1 + 1 / u conversion is done
y is certainly of the form
y '= p (x) y + r (x) y2 + g (x)
In this case p(x) = 0, r(x) = -a, and g(x) = b e-bx if I am reading the image correctly.
Do you mean you don't know the solution for the second order homogeneous ordinary differential equation which is the result of the replacement of y by
y = \(\displaystyle \frac{u'}{a u}\)
I haven't looked in detail at that equation so I'm not sure whether the substitution will help.
y '= p (x) y + r (x) y2 + g (x)
In this case p(x) = 0, r(x) = -a, and g(x) = b e-bx if I am reading the image correctly.
Do you mean you don't know the solution for the second order homogeneous ordinary differential equation which is the result of the replacement of y by
y = \(\displaystyle \frac{u'}{a u}\)
I haven't looked in detail at that equation so I'm not sure whether the substitution will help.