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Beliebt Rechnen >

(d^2y)/(dx^2)-2(dy)/(dx)+y=1+3x+x^2

Lösung

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

Lösung

y = c_{1} e^{x} + c_{2} x e^{x} + x^{2} + 7 x + 13

Schritte zur Lösung

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

Solve linear ODE:

y = c_{1} e^{x} + c_{2} x e^{x} + x^{2} + 7 x + 13

y = c_{1} e^{x} + c_{2} x e^{x} + x^{2} + 7 x + 13

Graph

Beliebte Beispiele

x^{''}-18x^'+81x=3te^{9t}

x^{^{''}} - 18 x^{^{'}} + 81 x = 3 t e^{9 t}

y^{''}+2y^'+y=2x^2+4x+2

y^{^{''}} + 2 y^{^{'}} + y = 2 x^{2} + 4 x + 2

y^{'''}+3y^{''}+3y^'+y=e-x

y^{^{'''}} + 3 y^{^{''}} + 3 y^{^{'}} + y = e - x

y^{''}-8y^'+16y=t^{-5}e^{4t}

y^{^{''}} - 8 y^{^{'}} + 16 y = t^{- 5} e^{4 t}

x^{''}+7x^'+12x=e^{2t}+cos(4t)

x^{^{''}} + 7 x^{^{'}} + 12 x = e^{2 t} + cos (4 t)