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Beliebt Rechnen >

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

Lösung

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

Lösung

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

Schritte zur Lösung

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

Solve linear ODE:

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

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

Graph

Beliebte Beispiele

y^{''}-4y^'-5y=2e^{2t}

y^{^{''}} - 4 y^{^{'}} - 5 y = 2 e^{2 t}

y^{''}+y=csc(x)cot(x)

y^{^{''}} + y = csc (x) cot (x)

y^{''}+4y=16tsin(2t)

y^{^{''}} + 4 y = 16 t sin (2 t)

y^{''}+2y^'-8y=4e^{-3x}-e^{-x}

y^{^{''}} + 2 y^{^{'}} - 8 y = 4 e^{- 3 x} - e^{- x}

4(d^2y)/(dx^2)-y=x*e^{x/2}

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