Sr Examen
Ecuación diferencial dx*(e^y*x+4*x^3-y)+dy*(e^y*x^2/2-x+1)=0
El profesor se sorprenderá mucho al ver tu solución correcta😉
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Solución
Ha introducido
[src]
2 d y(x)
x *--(y(x))*e
3 y(x) d dx d
-y(x) + 4*x + x*e - x*--(y(x)) + ----------------- + --(y(x)) = 0
dx 2 dx
$$4 x^{3} + \frac{x^{2} e^{y{\left(x \right)}} \frac{d}{d x} y{\left(x \right)}}{2} + x e^{y{\left(x \right)}} - x \frac{d}{d x} y{\left(x \right)} - y{\left(x \right)} + \frac{d}{d x} y{\left(x \right)} = 0$$
4*x^3 + x^2*exp(y)*y'/2 + x*exp(y) - x*y' - y + y' = 0
Respuesta
[src]
/ 4 \
| x - C1 + 2*(-1 + x)*log(x) |
| --------------------------- |
| -1 + x |
4 |-e |
x - C1 - (-1 + x)*W|------------------------------|
\ 2*(-1 + x) /
y(x) = ----------------------------------------------------
-1 + x
$$y{\left(x \right)} = \frac{- C_{1} + x^{4} - \left(x - 1\right) W\left(- \frac{e^{\frac{- C_{1} + x^{4} + 2 \left(x - 1\right) \log{\left(x \right)}}{x - 1}}}{2 \left(x - 1\right)}\right)}{x - 1}$$
Clasificación
1st exact
1st power series
lie group
1st exact Integral