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Beliebt Rechnen >

y^{''}+9y=(x^2+1)e^{3x}

Lösung

y^{^{''}} + 9 y = (x^{2} + 1) e^{3 x}

Lösung

y = c_{1} cos (3 x) + c_{2} sin (3 x) + \frac{e ^{3 x} x ^{2}}{18} - \frac{e ^{3 x} x}{27} + \frac{5}{81} e^{3 x}

Schritte zur Lösung

y^{''} (x) + 9 y = (x^{2} + 1) e^{3 x}

Solve linear ODE:

y = c_{1} cos (3 x) + c_{2} sin (3 x) + \frac{e ^{3 x} x ^{2}}{18} - \frac{e ^{3 x} x}{27} + \frac{5}{81} e^{3 x}

y = c_{1} cos (3 x) + c_{2} sin (3 x) + \frac{e ^{3 x} x ^{2}}{18} - \frac{e ^{3 x} x}{27} + \frac{5}{81} e^{3 x}

Graph

Beliebte Beispiele

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

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

3x^{''}+12x=sin(2t)

3 x^{^{''}} + 12 x = sin (2 t)

y^{'''}+2y^{''}=12x+4

y^{^{'''}} + 2 y^{^{''}} = 12 x + 4

y^{''}+25y=25sec^2(5t)

y^{^{''}} + 25 y = 25 sec^{2} (5 t)

x''+2x=8,x(pi)=0,x(0)=0

x^{''} + 2 x = 8, x (π) = 0, x (0) = 0