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Beliebt Rechnen >

y^{''}-2y^'+2y=5x^2-9x+5

Lösung

y^{^{''}} - 2 y^{^{'}} + 2 y = 5 x^{2} - 9 x + 5

Lösung

y = e^{x} (c_{1} cos (x) + c_{2} sin (x)) + \frac{5 x ^{2}}{2} + \frac{x}{2} + \frac{1}{2}

Schritte zur Lösung

y^{''} (x) - 2 y^{'} (x) + 2 y = 5 x^{2} - 9 x + 5

Solve linear ODE:

y = e^{x} (c_{1} cos (x) + c_{2} sin (x)) + \frac{5 x ^{2}}{2} + \frac{x}{2} + \frac{1}{2}

y = e^{x} (c_{1} cos (x) + c_{2} sin (x)) + \frac{5 x ^{2}}{2} + \frac{x}{2} + \frac{1}{2}

Graph

Beliebte Beispiele

y^{''}+5y=-5-6x+12x^2-5x^3+5x^4

y^{^{''}} + 5 y = - 5 - 6 x + 12 x^{2} - 5 x^{3} + 5 x^{4}

y^{''}+5y^'-6y=36x+98xe^x

y^{^{''}} + 5 y^{^{'}} - 6 y = 36 x + 98 x e^{x}

y^{''}+49y=49sec^2(7t)

y^{^{''}} + 49 y = 49 sec^{2} (7 t)

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

4y+7y^'+2y^{''}=10*cos(4x)

4 y + 7 y^{^{'}} + 2 y^{^{''}} = 10 \cdot cos (4 x)