Sr Examen
Ecuación diferencial dx*(x^4+6*x^2*y^2+y^4)+4*dy*x*(x^2+y^2)*y=0
El profesor se sorprenderá mucho al ver tu solución correcta😉
⌨
Solución
Ha introducido
[src]
4 4 2 2 3 d 3 d
x + y (x) + 6*x *y (x) + 4*x*y (x)*--(y(x)) + 4*x *--(y(x))*y(x) = 0
dx dx
$$x^{4} + 4 x^{3} y{\left(x \right)} \frac{d}{d x} y{\left(x \right)} + 6 x^{2} y^{2}{\left(x \right)} + 4 x y^{3}{\left(x \right)} \frac{d}{d x} y{\left(x \right)} + y^{4}{\left(x \right)} = 0$$
x^4 + 4*x^3*y*y' + 6*x^2*y^2 + 4*x*y^3*y' + y^4 = 0
Respuesta
[src]
___________________________________
/ _______________
/ ___ / / 5\
___ / 2 \/ 5 *\/ x*\C1 + 4*x /
-\/ 5 * / - 5*x - ------------------------
\/ x
y(x) = -------------------------------------------------
5
$$y{\left(x \right)} = - \frac{\sqrt{5} \sqrt{- 5 x^{2} - \frac{\sqrt{5} \sqrt{x \left(C_{1} + 4 x^{5}\right)}}{x}}}{5}$$
___________________________________
/ _______________
/ ___ / / 5\
___ / 2 \/ 5 *\/ x*\C1 + 4*x /
\/ 5 * / - 5*x - ------------------------
\/ x
y(x) = -----------------------------------------------
5
$$y{\left(x \right)} = \frac{\sqrt{5} \sqrt{- 5 x^{2} - \frac{\sqrt{5} \sqrt{x \left(C_{1} + 4 x^{5}\right)}}{x}}}{5}$$
___________________________________
/ _______________
/ ___ / / 5\
___ / 2 \/ 5 *\/ x*\C1 + 4*x /
-\/ 5 * / - 5*x + ------------------------
\/ x
y(x) = -------------------------------------------------
5
$$y{\left(x \right)} = - \frac{\sqrt{5} \sqrt{- 5 x^{2} + \frac{\sqrt{5} \sqrt{x \left(C_{1} + 4 x^{5}\right)}}{x}}}{5}$$
___________________________________
/ _______________
/ ___ / / 5\
___ / 2 \/ 5 *\/ x*\C1 + 4*x /
\/ 5 * / - 5*x + ------------------------
\/ x
y(x) = -----------------------------------------------
5
$$y{\left(x \right)} = \frac{\sqrt{5} \sqrt{- 5 x^{2} + \frac{\sqrt{5} \sqrt{x \left(C_{1} + 4 x^{5}\right)}}{x}}}{5}$$
Clasificación
1st exact
1st homogeneous coeff best
1st homogeneous coeff subs indep div dep
1st homogeneous coeff subs dep div indep
lie group
1st exact Integral
1st homogeneous coeff subs indep div dep Integral
1st homogeneous coeff subs dep div indep Integral