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Beliebt Rechnen >

(d^2y)/(dx^2)+4y=4x^2-4x

Lösung

\frac{d ^{2} y}{d x ^{2}} + 4 y = 4 x^{2} - 4 x

Lösung

y = c_{1} cos (2 x) + c_{2} sin (2 x) + x^{2} - x - \frac{1}{2}

Schritte zur Lösung

\frac{d ^{2} y}{d x ^{2}} + 4 y = 4 x^{2} - 4 x

Solve linear ODE:

y = c_{1} cos (2 x) + c_{2} sin (2 x) + x^{2} - x - \frac{1}{2}

y = c_{1} cos (2 x) + c_{2} sin (2 x) + x^{2} - x - \frac{1}{2}

Graph

Beliebte Beispiele

y^{''}-6y^'+9y=16e^7t,y(0)=7,y^'(0)=4

y^{^{''}} - 6 y^{^{'}} + 9 y = 16 e^{7} t, y (0) = 7, y^{^{'}} (0) = 4

y^{''}+6y+34=0,y(0)=3

y^{^{''}} + 6 y + 34 = 0, y (0) = 3

y^{''}+2y^'-3y=3e^{2t}

y^{^{''}} + 2 y^{^{'}} - 3 y = 3 e^{2 t}

y^{''}-3y^'=2x-2

y^{^{''}} - 3 y^{^{'}} = 2 x - 2

y^{''}+4y^'+5y=-15x+e-x

y^{^{''}} + 4 y^{^{'}} + 5 y = - 15 x + e - x