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Beliebt Rechnen >

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

Lösung

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

Lösung

y = c_{1} e^{2 x} + c_{2} x e^{2 x} + \frac{x ^{2}}{4} + \frac{x}{2} + \frac{3}{8}

Schritte zur Lösung

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

Solve linear ODE:

y = c_{1} e^{2 x} + c_{2} x e^{2 x} + \frac{x ^{2}}{4} + \frac{x}{2} + \frac{3}{8}

y = c_{1} e^{2 x} + c_{2} x e^{2 x} + \frac{x ^{2}}{4} + \frac{x}{2} + \frac{3}{8}

Graph

Beliebte Beispiele

taylor (x+1)^{1/2}

t a y l or (x + 1)^{\frac{1}{2}}

y^'=6x(y-1)^{2/3}

y^{^{'}} = 6 x (y - 1)^{\frac{2}{3}}

y^{''}+2sqrt(14)y^'+14y=0

y^{^{''}} + 214 y^{^{'}} + 14 y = 0

y^'+3/x y=x^2y^2

y^{^{'}} + \frac{3}{x} y = x^{2} y^{2}

(\partial)/(\partial x)(e^{3x}cos(2x))

\frac{\partial}{\partial x} (e^{3 x} cos (2 x))