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Beliebt Rechnen >

y^{''}-14y^'+49y=e^{7t}ln(t)

Lösung

y^{^{''}} - 14 y^{^{'}} + 49 y = e^{7 t} ln (t)

Lösung

y = c_{1} e^{7 t} + c_{2} t e^{7 t} + \frac{2 e ^{7 t} t ^{2} ln ( t ) - 3 e ^{7 t} t ^{2}}{4}

Schritte zur Lösung

y^{''} (t) - 14 y^{'} (t) + 49 y = e^{7 t} ln (t)

Solve linear ODE:

y = c_{1} e^{7 t} + c_{2} t e^{7 t} + \frac{2 e ^{7 t} t ^{2} ln ( t ) - 3 e ^{7 t} t ^{2}}{4}

y = c_{1} e^{7 t} + c_{2} t e^{7 t} + \frac{2 e ^{7 t} t ^{2} ln ( t ) - 3 e ^{7 t} t ^{2}}{4}

Graph

Beliebte Beispiele

y^{''}+2y= 1/(cos(sqrt(2x)))

y^{^{''}} + 2 y = \frac{1}{cos ( 2 x )}

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

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

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

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

y^{''}-3y=-48x^2e^{3x}

y^{^{''}} - 3 y = - 48 x^{2} e^{3 x}

y^{''}+16y=3cos(4t)

y^{^{''}} + 16 y = 3 cos (4 t)