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Beliebt Rechnen >

(t^2+16)^2y^'+2t(t^2+16)y=4,y(-2)=10

Lösung

(t^{2} + 16)^{2} y^{^{'}} + 2 t (t^{2} + 16) y = 4, y (- 2) = 10

Lösung

y = \frac{arctan ( \frac{t}{4} )}{t ^{2} + 16} + \frac{200 + arctan ( \frac{1}{2} )}{t ^{2} + 16}

Schritte zur Lösung

(t^{2} + 16)^{2} y^{'} (t) + 2 t (t^{2} + 16) y = 4

Solve linear ODE:

y = \frac{arctan ( \frac{t}{4} )}{t ^{2} + 16} + \frac{200 + arctan ( \frac{1}{2} )}{t ^{2} + 16}

y = \frac{arctan ( \frac{t}{4} )}{t ^{2} + 16} + \frac{200 + arctan ( \frac{1}{2} )}{t ^{2} + 16}

Beliebte Beispiele

integral of ((arctan(x))/(1+x^2))

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

integral of sqrt(36-4x^2)

\int 36 - 4 x^{2} d x

integral of 3xe^{-3x}

\int 3 x e^{- 3 x} d x

integral of e^{-x}sin(4x)

\int e^{- x} sin (4 x) d x

(x^2+1)y^'+6x(y-1)=0,y(0)=8

(x^{2} + 1) y^{^{'}} + 6 x (y - 1) = 0, y (0) = 8