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Beliebt Rechnen >

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

Lösung

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

Lösung

y = c_{1} + c_{2} e^{- x} + \frac{e ^{3 x} x ^{2}}{12} - \frac{7 e ^{3 x} x}{72} + \frac{37}{864} e^{3 x}

Schritte zur Lösung

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

Solve linear ODE:

y = c_{1} + c_{2} e^{- x} + \frac{e ^{3 x} x ^{2}}{12} - \frac{7 e ^{3 x} x}{72} + \frac{37}{864} e^{3 x}

y = c_{1} + c_{2} e^{- x} + \frac{e ^{3 x} x ^{2}}{12} - \frac{7 e ^{3 x} x}{72} + \frac{37}{864} e^{3 x}

Graph

Beliebte Beispiele

y^{'''}-4y^'=e^x

y^{^{'''}} - 4 y^{^{'}} = e^{x}

y^{''}+y^'+2y-x-3=0

y^{^{''}} + y^{^{'}} + 2 y - x - 3 = 0

y^{''''}+2y^{''}+y=9+cos(3t)

y^{^{''''}} + 2 y^{^{''}} + y = 9 + cos (3 t)

y^{''}-y=8e^{9t}+te^{9t}+5t^2e^{9t}

y^{^{''}} - y = 8 e^{9 t} + t e^{9 t} + 5 t^{2} e^{9 t}

14y^{''}+y^'+y=x^2-4x

14 y^{^{''}} + y^{^{'}} + y = x^{2} - 4 x