Sr Examen
Ecuación diferencial (1+exp(x))*y''+y'-(2+exp(x))y=0
El profesor se sorprenderá mucho al ver tu solución correcta😉
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Solución
Ha introducido
[src]
2
/ x\ d / x\ d
\1 + e /*---(y(x)) - \2 + e /*y(x) + --(y(x)) = 0
2 dx
dx
$$\left(e^{x} + 1\right) \frac{d^{2}}{d x^{2}} y{\left(x \right)} - \left(e^{x} + 2\right) y{\left(x \right)} + \frac{d}{d x} y{\left(x \right)} = 0$$
(exp(x) + 1)*y'' - (exp(x) + 2)*y + y' = 0
Respuesta
[src]
/ 2 3 4 4 2 x 3 x 4 x 4 2*x 4 x \ / 3 3 2 2 3 x 2 x \
| x x x x x *e x *e x *e x *e x *e | | x x x x x x *e x *e | / 6\
y(x) = C2*|1 + ------ - ------------------- + ------------------- + ----------------------------- + ---------- - ------------------- + ------------------- + -------------------- + -----------------------------| + C1*x*|1 - ---------- - ------------------- - ----------------------------- + ---------- + ------------------- - -------------------- + ----------| + O\x /
| x / x 2*x\ / x 2*x\ / x 2*x 3*x\ / x\ / x 2*x\ / x 2*x\ / x 2*x\ / x 2*x 3*x\| | / x\ / x 2*x\ / x 2*x 3*x\ / x\ / x 2*x\ / x 2*x\ / x\|
\ 1 + e 3*\1 + 2*e + e / 6*\1 + 2*e + e / 12*\1 + 3*e + 3*e + e / 2*\1 + e / 6*\1 + 2*e + e / 6*\1 + 2*e + e / 24*\1 + 2*e + e / 24*\1 + 3*e + 3*e + e // \ 2*\1 + e / 6*\1 + 2*e + e / 24*\1 + 3*e + 3*e + e / 3*\1 + e / 6*\1 + 2*e + e / 12*\1 + 2*e + e / 6*\1 + e //
$$y{\left(x \right)} = C_{2} \left(\frac{x^{4} e^{x}}{24 \left(e^{3 x} + 3 e^{2 x} + 3 e^{x} + 1\right)} + \frac{x^{4}}{12 \left(e^{3 x} + 3 e^{2 x} + 3 e^{x} + 1\right)} + \frac{x^{4} e^{2 x}}{24 \left(e^{2 x} + 2 e^{x} + 1\right)} + \frac{x^{4} e^{x}}{6 \left(e^{2 x} + 2 e^{x} + 1\right)} + \frac{x^{4}}{6 \left(e^{2 x} + 2 e^{x} + 1\right)} - \frac{x^{3} e^{x}}{6 \left(e^{2 x} + 2 e^{x} + 1\right)} - \frac{x^{3}}{3 \left(e^{2 x} + 2 e^{x} + 1\right)} + \frac{x^{2} e^{x}}{2 \left(e^{x} + 1\right)} + \frac{x^{2}}{e^{x} + 1} + 1\right) + C_{1} x \left(- \frac{x^{3}}{24 \left(e^{3 x} + 3 e^{2 x} + 3 e^{x} + 1\right)} - \frac{x^{3} e^{x}}{12 \left(e^{2 x} + 2 e^{x} + 1\right)} - \frac{x^{3}}{6 \left(e^{2 x} + 2 e^{x} + 1\right)} + \frac{x^{2}}{6 \left(e^{2 x} + 2 e^{x} + 1\right)} + \frac{x^{2} e^{x}}{6 \left(e^{x} + 1\right)} + \frac{x^{2}}{3 \left(e^{x} + 1\right)} - \frac{x}{2 \left(e^{x} + 1\right)} + 1\right) + O\left(x^{6}\right)$$
Clasificación
2nd power series ordinary