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Beliebt Rechnen >

y^{''}-2y^'+1=x^2

Lösung

y^{^{''}} - 2 y^{^{'}} + 1 = x^{2}

Lösung

y = c_{1} e^{2 x} + c_{2} - \frac{x ^{3}}{6} - \frac{x ^{2}}{4} + \frac{x}{4}

Schritte zur Lösung

y^{''} (x) - 2 y^{'} (x) + 1 = x^{2}

Solve linear ODE:

y = c_{1} e^{2 x} + c_{2} - \frac{x ^{3}}{6} - \frac{x ^{2}}{4} + \frac{x}{4}

y = c_{1} e^{2 x} + c_{2} - \frac{x ^{3}}{6} - \frac{x ^{2}}{4} + \frac{x}{4}

Graph

Beliebte Beispiele

y^{''}-4y^'+3y=3te^t,y(0)=1,y^'(0)=-5

y^{^{''}} - 4 y^{^{'}} + 3 y = 3 t e^{t}, y (0) = 1, y^{^{'}} (0) = - 5

y^{''}-3y^'-4y=8e^xcos(2x)

y^{^{''}} - 3 y^{^{'}} - 4 y = 8 e^{x} cos (2 x)

y^{''}+6y^'+5y=-1020sin(3t)

y^{^{''}} + 6 y^{^{'}} + 5 y = - 1020 sin (3 t)

(D^2+4D+8)y=4sin(2x)

(D^{2} + 4 D + 8) y = 4 sin (2 x)

y^{''}+9y=2t^2-2,y(0)=0,y^'(0)=-8

y^{^{''}} + 9 y = 2 t^{2} - 2, y (0) = 0, y^{^{'}} (0) = - 8