Sr Examen
Ecuación diferencial sqrt(y^2+1dx)=xydy
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Solución
Ha introducido
[src]
____________
/ 2
\/ dx + y (x) d
--------------- = x*--(y(x))*y(x)
dx dx
$$\frac{\sqrt{dx + y^{2}{\left(x \right)}}}{dx} = x y{\left(x \right)} \frac{d}{d x} y{\left(x \right)}$$
sqrt(dx + y^2)/dx = x*y*y'
Respuesta
[src]
__________________________________
/ 2
/ 2 log (x) 2*C1*log(x)
y(x) = - / C1 - dx + ------- + -----------
/ 2 dx
\/ dx
$$y{\left(x \right)} = - \sqrt{C_{1}^{2} + \frac{2 C_{1} \log{\left(x \right)}}{dx} - dx + \frac{\log{\left(x \right)}^{2}}{dx^{2}}}$$
__________________________________
/ 2
/ 2 log (x) 2*C1*log(x)
y(x) = / C1 - dx + ------- + -----------
/ 2 dx
\/ dx
$$y{\left(x \right)} = \sqrt{C_{1}^{2} + \frac{2 C_{1} \log{\left(x \right)}}{dx} - dx + \frac{\log{\left(x \right)}^{2}}{dx^{2}}}$$
Clasificación
factorable
separable
lie group
separable Integral