Sr Examen
Ecuación diferencial dy/y^6=x^3dx
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Solución
Ha introducido
[src]
d --(y(x)) dx 3 -------- = x 6 y (x)
$$\frac{\frac{d}{d x} y{\left(x \right)}}{y^{6}{\left(x \right)}} = x^{3}$$
y'/y^6 = x^3
Respuesta
[src]
___________
2/5 / -1
y(x) = 2 * / ---------
5 / 4
\/ C1 + 5*x
$$y{\left(x \right)} = 2^{\frac{2}{5}} \sqrt[5]{- \frac{1}{C_{1} + 5 x^{4}}}$$
_________ / ___________\
/ -1 | 2/5 4/5 2/5 3/10 9/10 4/5 / ___ |
/ ------- *\- 2 *5 + 5*2 *5 - I*2 *5 *\/ 5 + \/ 5 /
5 / 4
\/ C1 + x
y(x) = -------------------------------------------------------------------------
20
$$y{\left(x \right)} = \frac{\sqrt[5]{- \frac{1}{C_{1} + x^{4}}} \left(- 2^{\frac{2}{5}} \cdot 5^{\frac{4}{5}} + 5 \cdot 2^{\frac{2}{5}} \cdot 5^{\frac{3}{10}} - 2^{\frac{9}{10}} \cdot 5^{\frac{4}{5}} i \sqrt{\sqrt{5} + 5}\right)}{20}$$
_________ / ___________\
/ -1 | 2/5 4/5 2/5 3/10 9/10 4/5 / ___ |
/ ------- *\- 2 *5 + 5*2 *5 + I*2 *5 *\/ 5 + \/ 5 /
5 / 4
\/ C1 + x
y(x) = -------------------------------------------------------------------------
20
$$y{\left(x \right)} = \frac{\sqrt[5]{- \frac{1}{C_{1} + x^{4}}} \left(- 2^{\frac{2}{5}} \cdot 5^{\frac{4}{5}} + 5 \cdot 2^{\frac{2}{5}} \cdot 5^{\frac{3}{10}} + 2^{\frac{9}{10}} \cdot 5^{\frac{4}{5}} i \sqrt{\sqrt{5} + 5}\right)}{20}$$
_________ / ___________\
/ -1 | 2/5 4/5 2/5 3/10 9/10 4/5 / ___ |
/ ------- *\- 2 *5 - 5*2 *5 - I*2 *5 *\/ 5 - \/ 5 /
5 / 4
\/ C1 + x
y(x) = -------------------------------------------------------------------------
20
$$y{\left(x \right)} = \frac{\sqrt[5]{- \frac{1}{C_{1} + x^{4}}} \left(- 5 \cdot 2^{\frac{2}{5}} \cdot 5^{\frac{3}{10}} - 2^{\frac{2}{5}} \cdot 5^{\frac{4}{5}} - 2^{\frac{9}{10}} \cdot 5^{\frac{4}{5}} i \sqrt{5 - \sqrt{5}}\right)}{20}$$
_________ / ___________\
/ -1 | 2/5 4/5 2/5 3/10 9/10 4/5 / ___ |
/ ------- *\- 2 *5 - 5*2 *5 + I*2 *5 *\/ 5 - \/ 5 /
5 / 4
\/ C1 + x
y(x) = -------------------------------------------------------------------------
20
$$y{\left(x \right)} = \frac{\sqrt[5]{- \frac{1}{C_{1} + x^{4}}} \left(- 5 \cdot 2^{\frac{2}{5}} \cdot 5^{\frac{3}{10}} - 2^{\frac{2}{5}} \cdot 5^{\frac{4}{5}} + 2^{\frac{9}{10}} \cdot 5^{\frac{4}{5}} i \sqrt{5 - \sqrt{5}}\right)}{20}$$
Clasificación
separable
1st exact
Bernoulli
separable reduced
1st power series
lie group
separable Integral
1st exact Integral
Bernoulli Integral
separable reduced Integral