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Beliebt Rechnen >

5y^{''}+10y^'=3x^2

Lösung

5 y^{^{''}} + 10 y^{^{'}} = 3 x^{2}

Lösung

y = c_{1} + c_{2} e^{- 2 x} + \frac{x ^{3}}{10} - \frac{3 x ^{2}}{20} + \frac{3 x}{20}

Schritte zur Lösung

5 y^{''} (x) + 10 y^{'} (x) = 3 x^{2}

Solve linear ODE:

y = c_{1} + c_{2} e^{- 2 x} + \frac{x ^{3}}{10} - \frac{3 x ^{2}}{20} + \frac{3 x}{20}

y = c_{1} + c_{2} e^{- 2 x} + \frac{x ^{3}}{10} - \frac{3 x ^{2}}{20} + \frac{3 x}{20}

Graph

Beliebte Beispiele

x^{''}+4x^'+3x=sin(e^t)

x^{^{''}} + 4 x^{^{'}} + 3 x = sin (e^{t})

y^{''}+4y=4sec^2(2x)

y^{^{''}} + 4 y = 4 sec^{2} (2 x)

(d^2y)/(dx^2)+(dy)/(dx)=x

\frac{d ^{2} y}{d x ^{2}} + \frac{d y}{d x} = x

y^{''}+4y+4y=(3+x)e^{-2x}

y^{^{''}} + 4 y + 4 y = (3 + x) e^{- 2 x}

y^{''}-6y^'+8y=3e^{-2x}+2x

y^{^{''}} - 6 y^{^{'}} + 8 y = 3 e^{- 2 x} + 2 x