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Beliebt Rechnen >

x^2(dy)/(dx)=sqrt(y)(4x+3)

Lösung

x^{2} \frac{d y}{d x} = y (4 x + 3)

Lösung

y = - \frac{3 c _{1}}{2 x} - \frac{6 ln ( x )}{x} + \frac{9}{4 x ^{2}} + \frac{c _{1}^{2}}{4} + 4 ln^{2} (x) + 2 c_{1} ln (x)

Schritte zur Lösung

x^{2} \frac{d y}{d x} = y (4 x + 3)

Solve separable ODE:

y = - \frac{3 c _{1}}{2 x} - \frac{6 ln ( x )}{x} + \frac{9}{4 x ^{2}} + \frac{c _{1}^{2}}{4} + 4 ln^{2} (x) + 2 c_{1} ln (x)

y = - \frac{3 c _{1}}{2 x} - \frac{6 ln ( x )}{x} + \frac{9}{4 x ^{2}} + \frac{c _{1}^{2}}{4} + 4 ln^{2} (x) + 2 c_{1} ln (x)

Graph

Beliebte Beispiele

(\partial)/(\partial x)(-sin(xy))

\frac{\partial}{\partial x} (- sin (x y))

integral of x/((x^2-1))

\int \frac{x}{( x ^{2} - 1 )} d x

integral of 8x^2ln(x)

\int 8 x^{2} ln (x) d x

d/(dt)(sin(t)+cos(t))

\frac{d}{d t} (sin (t) + cos (t))

fläche y=x^3,(-1,2)

a re a y = x^{3}, (- 1, 2)