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Beliebt Rechnen >

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

Lösung

y^{^{''}} + 9 y = x^{2} 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{1}{162} e^{3 x}

Schritte zur Lösung

y^{''} (x) + 9 y = x^{2} 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{1}{162} 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{1}{162} e^{3 x}

Graph

Beliebte Beispiele

6y^{''}-y^'-7y=-7

6 y^{^{''}} - y^{^{'}} - 7 y = - 7

y^{''}-9y=(x^2-7)sin(3x)

y^{^{''}} - 9 y = (x^{2} - 7) sin (3 x)

y^{''}+36y=csc^2(6x)

y^{^{''}} + 36 y = csc^{2} (6 x)

y^{''}+6y^'-40y=1-3x+x^2

y^{^{''}} + 6 y^{^{'}} - 40 y = 1 - 3 x + x^{2}

y^{''}+10y^'+25y=e^{2x},y(0)=0,y^'(0)=0

y^{^{''}} + 10 y^{^{'}} + 25 y = e^{2 x}, y (0) = 0, y^{^{'}} (0) = 0