Sr Examen

Otras calculadoras

Ecuación diferencial yy^(1/2)dx-(2xx^(1/2)+xy^(1/2))dy=0

El profesor se sorprenderá mucho al ver tu solución correcta😉

v

Para el problema de Cauchy:

y() =
y'() =
y''() =
y'''() =
y''''() =

Gráfico:

interior superior

Solución

Ha introducido [src]
 3/2         3/2 d              ______ d           
y   (x) - 2*x   *--(y(x)) - x*\/ y(x) *--(y(x)) = 0
                 dx                    dx          
$$- 2 x^{\frac{3}{2}} \frac{d}{d x} y{\left(x \right)} - x \sqrt{y{\left(x \right)}} \frac{d}{d x} y{\left(x \right)} + y^{\frac{3}{2}}{\left(x \right)} = 0$$
-2*x^(3/2)*y' - x*sqrt(y)*y' + y^(3/2) = 0
Respuesta [src]
                /      _____ \
                |     /  C1  |
                |    /  e    |
                |-  /   ---  |
                | \/     x   |
        C1 - 2*W|------------|
                \     2      /
y(x) = e                      
$$y{\left(x \right)} = e^{C_{1} - 2 W\left(- \frac{\sqrt{\frac{e^{C_{1}}}{x}}}{2}\right)}$$
                /     _____\
                |    /  C1 |
                |   /  e   |
                |  /   --- |
                |\/     x  |
        C1 - 2*W|----------|
                \    2     /
y(x) = e                    
$$y{\left(x \right)} = e^{C_{1} - 2 W\left(\frac{\sqrt{\frac{e^{C_{1}}}{x}}}{2}\right)}$$
Gráfico para el problema de Cauchy
Clasificación
factorable
1st homogeneous coeff best
1st homogeneous coeff subs indep div dep
1st homogeneous coeff subs dep div indep
lie group
1st homogeneous coeff subs indep div dep Integral
1st homogeneous coeff subs dep div indep Integral
Respuesta numérica [src]
(x, y):
(-10.0, 0.75)
(-7.777777777777778, nan)
(-5.555555555555555, nan)
(-3.333333333333333, nan)
(-1.1111111111111107, nan)
(1.1111111111111107, nan)
(3.333333333333334, nan)
(5.555555555555557, nan)
(7.777777777777779, nan)
(10.0, nan)
(10.0, nan)