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Beliebt Rechnen >

y^{''}+4y^'-5y=10x^2+9e^x

Lösung

y^{^{''}} + 4 y^{^{'}} - 5 y = 10 x^{2} + 9 e^{x}

Lösung

y = c_{1} e^{x} + c_{2} e^{- 5 x} - 2 x^{2} - \frac{16 x}{5} - \frac{84}{25} + \frac{3 e ^{x} x}{2}

Schritte zur Lösung

y^{''} (x) + 4 y^{'} (x) - 5 y = 10 x^{2} + 9 e^{x}

Solve linear ODE:

y = c_{1} e^{x} + c_{2} e^{- 5 x} - 2 x^{2} - \frac{16 x}{5} - \frac{84}{25} + \frac{3 e ^{x} x}{2}

y = c_{1} e^{x} + c_{2} e^{- 5 x} - 2 x^{2} - \frac{16 x}{5} - \frac{84}{25} + \frac{3 e ^{x} x}{2}

Graph

Beliebte Beispiele

(d-1)^2(d-3)^3y=e^3x

(d - 1)^{2} (d - 3)^{3} y = e^{3} x

y^{''}+y^'-6y=50xe^x

y^{^{''}} + y^{^{'}} - 6 y = 50 x e^{x}

y^{^{''}} - 9 y = 1

y^{''}-3y^'-4y=t^2,y(0)=1,y^'(0)=4

y^{^{''}} - 3 y^{^{'}} - 4 y = t^{2}, y (0) = 1, y^{^{'}} (0) = 4

y^{''}+9y=sin(3t),y(0)=1,y^'(0)=1

y^{^{''}} + 9 y = sin (3 t), y (0) = 1, y^{^{'}} (0) = 1