Sr Examen
Ecuación diferencial dx*(e^(2*x)+x^3*y^5/5-y)+dy*(x^4*y^4/4-x+2)=0
El profesor se sorprenderá mucho al ver tu solución correcta😉
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Solución
Ha introducido
[src]
4 4 d
3 5 x *y (x)*--(y(x))
d d x *y (x) dx 2*x
-y(x) + 2*--(y(x)) - x*--(y(x)) + -------- + ----------------- + e = 0
dx dx 5 4
$$\frac{x^{4} y^{4}{\left(x \right)} \frac{d}{d x} y{\left(x \right)}}{4} + \frac{x^{3} y^{5}{\left(x \right)}}{5} - x \frac{d}{d x} y{\left(x \right)} - y{\left(x \right)} + e^{2 x} + 2 \frac{d}{d x} y{\left(x \right)} = 0$$
x^4*y^4*y'/4 + x^3*y^5/5 - x*y' - y + exp(2*x) + 2*y' = 0
Respuesta
[src]
2*x 4 5 e x *y (x) ---- + 2*y(x) - x*y(x) + -------- = C1 2 20
$$\frac{x^{4} y^{5}{\left(x \right)}}{20} - x y{\left(x \right)} + 2 y{\left(x \right)} + \frac{e^{2 x}}{2} = C_{1}$$
Clasificación
1st exact
1st power series
lie group
1st exact Integral