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Beliebt Rechnen >

(d^2y)/(dx^2)+14(dy)/(dx)+49y=4e^{5x}

Lösung

\frac{d ^{2} y}{d x ^{2}} + 14 \frac{d y}{d x} + 49 y = 4 e^{5 x}

Lösung

y = c_{1} e^{- 7 x} + c_{2} x e^{- 7 x} + \frac{1}{36} e^{5 x}

Schritte zur Lösung

\frac{d ^{2} y}{d x ^{2}} + 14 \frac{d y}{d x} + 49 y = 4 e^{5 x}

Solve linear ODE:

y = c_{1} e^{- 7 x} + c_{2} x e^{- 7 x} + \frac{1}{36} e^{5 x}

y = c_{1} e^{- 7 x} + c_{2} x e^{- 7 x} + \frac{1}{36} e^{5 x}

Graph

Beliebte Beispiele

y^{^{''}} + 3 y + 2 = 0

y^{''}-14y^'+49y=21x+6

y^{^{''}} - 14 y^{^{'}} + 49 y = 21 x + 6

y^{''}-8y^'+16=0,y(0)=4,y(1)=5

y^{^{''}} - 8 y^{^{'}} + 16 = 0, y (0) = 4, y (1) = 5

4y^{''}+6y^'+25y=4cos(2t)

4 y^{^{''}} + 6 y^{^{'}} + 25 y = 4 cos (2 t)

y^{''}+8y^'+6y=18x^2

y^{^{''}} + 8 y^{^{'}} + 6 y = 18 x^{2}