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Beliebt Rechnen >

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

Lösung

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

Lösung

y = c_{1} e^{2 x} + c_{2} x e^{2 x} - 2 e^{2 x} x + 2 e^{2 x} x ln (x)

Schritte zur Lösung

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

Solve linear ODE:

y = c_{1} e^{2 x} + c_{2} x e^{2 x} - 2 e^{2 x} x + 2 e^{2 x} x ln (x)

y = c_{1} e^{2 x} + c_{2} x e^{2 x} - 2 e^{2 x} x + 2 e^{2 x} x ln (x)

Graph

Beliebte Beispiele

y^{''}+3y^'-4y=6e^x

y^{^{''}} + 3 y^{^{'}} - 4 y = 6 e^{x}

y^{''}-2y^'+2y=3e^xsec(x)

y^{^{''}} - 2 y^{^{'}} + 2 y = 3 e^{x} sec (x)

y^{''}-3y^'-4y=10e^t-250cos(3t)

y^{^{''}} - 3 y^{^{'}} - 4 y = 10 e^{t} - 250 cos (3 t)

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

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

y^{''}+2y^'+y=1-\H(t-1)

y^{^{''}} + 2 y^{^{'}} + y = 1 - H (t - 1)