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Beliebt Rechnen >

linear y^{''}-14y^'+49y=x^2

Lösung

linear

y^{^{''}} - 14 y^{^{'}} + 49 y = x^{2}

Lösung

y = c_{1} e^{7 x} + c_{2} x e^{7 x} + \frac{x ^{2}}{49} + \frac{4 x}{343} + \frac{6}{2401}

Schritte zur Lösung

y^{''} (x) - 14 y^{'} (x) + 49 y = x^{2}

Solve linear ODE:

y = c_{1} e^{7 x} + c_{2} x e^{7 x} + \frac{x ^{2}}{49} + \frac{4 x}{343} + \frac{6}{2401}

y = c_{1} e^{7 x} + c_{2} x e^{7 x} + \frac{x ^{2}}{49} + \frac{4 x}{343} + \frac{6}{2401}

Graph

Beliebte Beispiele

y^{''}+16y^'=x+e^{2x}

y^{^{''}} + 16 y^{^{'}} = x + e^{2 x}

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

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

4y^{''}-2y^'=4x,y(0)=2,y^'(0)=1

4 y^{^{''}} - 2 y^{^{'}} = 4 x, y (0) = 2, y^{^{'}} (0) = 1

y^{''}-4y^'-12y=(4x+7)e^{-2x}

y^{^{''}} - 4 y^{^{'}} - 12 y = (4 x + 7) e^{- 2 x}

y^{''}+4y^'+5y=2e^{3x}

y^{^{''}} + 4 y^{^{'}} + 5 y = 2 e^{3 x}