Sr Examen
Ecuación diferencial y'=f(ax+by)
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Solución
Ha introducido
[src]
d --(y(x)) = f*(a*x + b*y(x)) dx
$$\frac{d}{d x} y{\left(x \right)} = f \left(a x + b y{\left(x \right)}\right)$$
y' = f*(a*x + b*y)
Respuesta
[src]
/ // -b*f*x \\
| ||(-a - a*b*f*x)*e 2 ||
| ||---------------------- for f*b != 0||
| || 2 ||
| || b *f || b*f*x
y(x) = |C1 + |< ||*e
| || 2 ||
| || a*f*x ||
| || ------ otherwise ||
| || 2 ||
\ \\ //
$$y{\left(x \right)} = \left(C_{1} + \begin{cases} \frac{\left(- a b f x - a\right) e^{- b f x}}{b^{2} f} & \text{for}\: b^{2} f \neq 0 \\\frac{a f x^{2}}{2} & \text{otherwise} \end{cases}\right) e^{b f x}$$
Clasificación
1st linear
Bernoulli
almost linear
1st power series
lie group
nth linear constant coeff undetermined coefficients
nth linear constant coeff variation of parameters
1st linear Integral
Bernoulli Integral
almost linear Integral
nth linear constant coeff variation of parameters Integral