Sr Examen

Ecuación diferencial ydy=(-9x+1+2*y)*dx

El profesor se sorprenderá mucho al ver tu solución correcta😉

v

Para el problema de Cauchy:

y() =
y'() =
y''() =
y'''() =
y''''() =

Gráfico:

interior superior

Solución

Ha introducido [src]
d                               
--(y(x))*y(x) = 1 - 9*x + 2*y(x)
dx                              
$$y{\left(x \right)} \frac{d}{d x} y{\left(x \right)} = - 9 x + 2 y{\left(x \right)} + 1$$
y*y' = -9*x + 2*y + 1
Respuesta [src]
                                                                         /  ___ /      y(x)  \\
                                                                         |\/ 2 *|1 - --------||
                        /      ____________________________\     ___     |      \    -1/9 + x/|
                        |     /         2                  |   \/ 2 *atan|--------------------|
                        |    /         y (x)       2*y(x)  |             \         4          /
log(-1/9 + x) = C1 - log|   /   9 + ----------- - -------- | + --------------------------------
                        |  /                  2   -1/9 + x |                  4                
                        \\/         (-1/9 + x)             /                                   
$$\log{\left(x - \frac{1}{9} \right)} = C_{1} - \log{\left(\sqrt{9 - \frac{2 y{\left(x \right)}}{x - \frac{1}{9}} + \frac{y^{2}{\left(x \right)}}{\left(x - \frac{1}{9}\right)^{2}}} \right)} + \frac{\sqrt{2} \operatorname{atan}{\left(\frac{\sqrt{2} \left(1 - \frac{y{\left(x \right)}}{x - \frac{1}{9}}\right)}{4} \right)}}{4}$$
Gráfico para el problema de Cauchy
Clasificación
linear coefficients
1st power series
lie group
linear coefficients Integral
Respuesta numérica [src]
(x, y):
(-10.0, 0.75)
(-7.777777777777778, 22.13046315034495)
(-5.555555555555555, 31.662457964232622)
(-3.333333333333333, 38.71491494153402)
(-1.1111111111111107, 44.29464268725485)
(1.1111111111111107, 48.79446919115949)
(3.333333333333334, 52.41051599808383)
(5.555555555555557, 55.25005810338515)
(7.777777777777779, 57.37075194506625)
(10.0, 58.797155447465116)
(10.0, 58.797155447465116)