Sr Examen
Ecuación diferencial dy*(e^2*x+1)*y^2=dx*e^x
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Solución
Ha introducido
[src]
2 d 2 d 2 x
y (x)*--(y(x)) + x*y (x)*--(y(x))*e = e
dx dx
$$x y^{2}{\left(x \right)} e^{2} \frac{d}{d x} y{\left(x \right)} + y^{2}{\left(x \right)} \frac{d}{d x} y{\left(x \right)} = e^{x}$$
x*y^2*exp(2)*y' + y^2*y' = exp(x)
Respuesta
[src]
_______________________
/ /
/ |
/ | x
/ | e
y(x) = / C1 + 3* | -------- dx
/ | 2
/ | 1 + x*e
3 / |
\/ /
$$y{\left(x \right)} = \sqrt[3]{C_{1} + 3 \int \frac{e^{x}}{x e^{2} + 1}\, dx}$$
_____________________
/ /
/ |
/ | x
/ | e / 3 ___ 5/6\
/ C1 + | -------- dx *\- \/ 3 - I*3 /
/ | 2
/ | 1 + x*e
3 / |
\/ /
y(x) = --------------------------------------------------
2
$$y{\left(x \right)} = \frac{\left(- \sqrt[3]{3} - 3^{\frac{5}{6}} i\right) \sqrt[3]{C_{1} + \int \frac{e^{x}}{x e^{2} + 1}\, dx}}{2}$$
_____________________
/ /
/ |
/ | x
/ | e / 3 ___ 5/6\
/ C1 + | -------- dx *\- \/ 3 + I*3 /
/ | 2
/ | 1 + x*e
3 / |
\/ /
y(x) = --------------------------------------------------
2
$$y{\left(x \right)} = \frac{\left(- \sqrt[3]{3} + 3^{\frac{5}{6}} i\right) \sqrt[3]{C_{1} + \int \frac{e^{x}}{x e^{2} + 1}\, dx}}{2}$$
Clasificación
separable
1st exact
Bernoulli
1st power series
lie group
separable Integral
1st exact Integral
Bernoulli Integral