Sr Examen
Ecuación diferencial (sinx+y)dy+(ycosx−x^2)dx=0x'=ycosx-x^2
El profesor se sorprenderá mucho al ver tu solución correcta😉
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Solución
Ha introducido
[src]
2 d d
- x + --(y(x))*sin(x) + --(y(x))*y(x) + cos(x)*y(x) = 0
dx dx
$$- x^{2} + y{\left(x \right)} \cos{\left(x \right)} + y{\left(x \right)} \frac{d}{d x} y{\left(x \right)} + \sin{\left(x \right)} \frac{d}{d x} y{\left(x \right)} = 0$$
-x^2 + y*cos(x) + y*y' + sin(x)*y' = 0
Respuesta
[src]
_______________________
/ 3 2
\/ C1 + 6*x + 9*sin (x)
y(x) = -sin(x) - --------------------------
3
$$y{\left(x \right)} = - \frac{\sqrt{C_{1} + 6 x^{3} + 9 \sin^{2}{\left(x \right)}}}{3} - \sin{\left(x \right)}$$
_______________________
/ 3 2
\/ C1 + 6*x + 9*sin (x)
y(x) = -sin(x) + --------------------------
3
$$y{\left(x \right)} = \frac{\sqrt{C_{1} + 6 x^{3} + 9 \sin^{2}{\left(x \right)}}}{3} - \sin{\left(x \right)}$$
Gráfico para el problema de Cauchy
Clasificación
1st exact
1st power series
lie group
1st exact Integral
Respuesta numérica
[src]
(x, y):
(-10.0, 0.75)
(-7.777777777777778, 19.84829752882298)
(-5.555555555555555, 22.875836073738604)
(-3.333333333333333, 25.174569286366353)
(-1.1111111111111107, 26.740607616013182)
(1.1111111111111107, 24.983585344943883)
(3.333333333333334, 26.511147523747056)
(5.555555555555557, 28.64365292061021)
(7.777777777777779, 30.35112388422979)
(10.0, 37.081778050707065)
(10.0, 37.081778050707065)