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Beliebt Rechnen >

4y^{''}+20y^'+25y=0,y(0)=1,y^'(0)=2

Lösung

4 y^{^{''}} + 20 y^{^{'}} + 25 y = 0, y (0) = 1, y^{^{'}} (0) = 2

Lösung

y = e^{- \frac{5 t}{2}} + \frac{9 e ^{- \frac{5 t}{2}} t}{2}

Schritte zur Lösung

4 y^{''} (t) + 20 y^{'} (t) + 25 y = 0

Solve linear ODE:

y = e^{- \frac{5 t}{2}} + \frac{9 e ^{- \frac{5 t}{2}} t}{2}

y = e^{- \frac{5 t}{2}} + \frac{9 e ^{- \frac{5 t}{2}} t}{2}

Graph

Beliebte Beispiele

(D^3-3D^2+4)y=0

(D^{3} - 3 D^{2} + 4) y = 0

y^{''}-24y^'+αy=0,y(0)=1,y^'(0)=22

y^{^{''}} - 24 y^{^{'}} + α y = 0, y (0) = 1, y^{^{'}} (0) = 22

6(d^2y)/(dx^2)-(dy)/(dx)-y=0

6 \frac{d ^{2} y}{d x ^{2}} - \frac{d y}{d x} - y = 0

y^{'''}-y^{''}+4y^'+6y=0

y^{^{'''}} - y^{^{''}} + 4 y^{^{'}} + 6 y = 0

(D^{2} + 1) y = 0