Sr Examen
Ecuación diferencial 4*tan(x)*sec(x)^2*y'+2*sec(x)^2*y''+1=0
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Solución
Ha introducido
[src]
2
2 d 2 d
1 + 2*sec (x)*---(y(x)) + 4*sec (x)*--(y(x))*tan(x) = 0
2 dx
dx
$$4 \tan{\left(x \right)} \sec^{2}{\left(x \right)} \frac{d}{d x} y{\left(x \right)} + 2 \sec^{2}{\left(x \right)} \frac{d^{2}}{d x^{2}} y{\left(x \right)} + 1 = 0$$
4*tan(x)*sec(x)^2*y' + 2*sec(x)^2*y'' + 1 = 0
Respuesta
[src]
2 2 2 2 2
sin (x) x *cos (x) x *sin (x) 2 2 x*cos(x)*sin(x)
y(x) = C1 + ------- - ---------- - ---------- + C2*x*cos (x) + C2*x*sin (x) + C2*cos(x)*sin(x) - ---------------
8 8 8 4
$$y{\left(x \right)} = C_{1} + C_{2} x \sin^{2}{\left(x \right)} + C_{2} x \cos^{2}{\left(x \right)} + C_{2} \sin{\left(x \right)} \cos{\left(x \right)} - \frac{x^{2} \sin^{2}{\left(x \right)}}{8} - \frac{x^{2} \cos^{2}{\left(x \right)}}{8} - \frac{x \sin{\left(x \right)} \cos{\left(x \right)}}{4} + \frac{\sin^{2}{\left(x \right)}}{8}$$
Clasificación
nth order reducible