Sr Examen
Ecuación diferencial dx*(x^3*y^2+x*y-cos(x))+dy*(x^4*y/2+x^2/2-2)=0
El profesor se sorprenderá mucho al ver tu solución correcta😉
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Solución
Ha introducido
[src]
2 d 4 d
x *--(y(x)) x *--(y(x))*y(x)
d 3 2 dx dx
-cos(x) - 2*--(y(x)) + x*y(x) + x *y (x) + ----------- + ---------------- = 0
dx 2 2
$$\frac{x^{4} y{\left(x \right)} \frac{d}{d x} y{\left(x \right)}}{2} + x^{3} y^{2}{\left(x \right)} + \frac{x^{2} \frac{d}{d x} y{\left(x \right)}}{2} + x y{\left(x \right)} - \cos{\left(x \right)} - 2 \frac{d}{d x} y{\left(x \right)} = 0$$
x^4*y*y'/2 + x^3*y^2 + x^2*y'/2 + x*y - cos(x) - 2*y' = 0
Respuesta
[src]
______________________________________
/ 4 2 4 4
4 \/ 16 + x - 8*x + C1*x + 4*x *sin(x)
-1 + -- - -----------------------------------------
2 2
x x
y(x) = ---------------------------------------------------
2
x
$$y{\left(x \right)} = \frac{-1 - \frac{\sqrt{C_{1} x^{4} + 4 x^{4} \sin{\left(x \right)} + x^{4} - 8 x^{2} + 16}}{x^{2}} + \frac{4}{x^{2}}}{x^{2}}$$
______________________________________
/ 4 2 4 4
4 \/ 16 + x - 8*x + C1*x + 4*x *sin(x)
-1 + -- + -----------------------------------------
2 2
x x
y(x) = ---------------------------------------------------
2
x
$$y{\left(x \right)} = \frac{-1 + \frac{\sqrt{C_{1} x^{4} + 4 x^{4} \sin{\left(x \right)} + x^{4} - 8 x^{2} + 16}}{x^{2}} + \frac{4}{x^{2}}}{x^{2}}$$
Clasificación
1st exact
1st power series
lie group
1st exact Integral