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Beliebt Rechnen >

(dy)/(dx)=(4y^{3/4})/(x^2+1),y(0)=1

Lösung

\frac{d y}{d x} = \frac{4 y ^{\frac{3}{4}}}{x ^{2} + 1}, y (0) = 1

Lösung

y = arctan^{4} (x) + 4 arctan^{3} (x) + 6 arctan^{2} (x) + 4 arctan (x) + 1

Schritte zur Lösung

\frac{d y}{d x} = \frac{4 y ^{\frac{3}{4}}}{x ^{2} + 1}

Solve separable ODE:

y = arctan^{4} (x) + 4 arctan^{3} (x) + 6 arctan^{2} (x) + 4 arctan (x) + 1

y = arctan^{4} (x) + 4 arctan^{3} (x) + 6 arctan^{2} (x) + 4 arctan (x) + 1

Graph

Beliebte Beispiele

y^{^{'}} = (1 + y^{2}) e^{x}

y^{^{'}} = x^{2} - 3 x^{2} y

(dy)/(dx)=(2y+5)/(-5x-2)

\frac{d y}{d x} = \frac{2 y + 5}{- 5 x - 2}

(dy)/(dx)y=sqrt(x^2+8)

\frac{d y}{d x} y = x^{2} + 8

(ln(y))^3(dy)/(dx)=x^3y,y(1)=e^2

(ln (y))^{3} \frac{d y}{d x} = x^{3} y, y (1) = e^{2}