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Beliebt Rechnen >

(dy)/(dx)=2ysqrt(16-x^2),y(0)=1

Lösung

\frac{d y}{d x} = 2 y 16 - x^{2}, y (0) = 1

Lösung

y = e^{16 (a r c s i n (\frac{x}{4}) + \frac{1}{2} s i n (2 a r c s i n (\frac{x}{4})))}

Schritte zur Lösung

\frac{d y}{d x} = 2 y 16 - x^{2}

Solve separable ODE:

y = e^{16 (a r c s i n (\frac{x}{4}) + \frac{1}{2} s i n (2 a r c s i n (\frac{x}{4})))}

y = e^{16 (a r c s i n (\frac{x}{4}) + \frac{1}{2} s i n (2 a r c s i n (\frac{x}{4})))}

Graph

Beliebte Beispiele

derivative of ln(16-x^2)

\frac{d}{d x} (ln (16 - x^{2}))

integral of 2(2+x^2)^{3/2}

\int 2 (2 + x^{2})^{\frac{3}{2}} d x

integral of x^2(x^3+6)^6

\int x^{2} (x^{3} + 6)^{6} d x

tangent f(x)=sqrt(1+x^3),\at x=2

t an g e n t f (x) = 1 + x^{3}, at x = 2

\frac{d y}{d x} = x - 1