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Beliebt Rechnen >

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

Lösung

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

Lösung

y = c_{1} + c_{2} e^{- 3 x} + \frac{x ^{3}}{9} - \frac{x ^{2}}{9} + \frac{2 x}{27}

Schritte zur Lösung

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

Solve linear ODE:

y = c_{1} + c_{2} e^{- 3 x} + \frac{x ^{3}}{9} - \frac{x ^{2}}{9} + \frac{2 x}{27}

y = c_{1} + c_{2} e^{- 3 x} + \frac{x ^{3}}{9} - \frac{x ^{2}}{9} + \frac{2 x}{27}

Graph

Beliebte Beispiele

(d^2y)/(dx^2)+9y=sin(3x)

\frac{d ^{2} y}{d x ^{2}} + 9 y = sin (3 x)

y^{''}+4y^'+3y=cos(t)

y^{^{''}} + 4 y^{^{'}} + 3 y = cos (t)

x^{''}+4x=-5sin(2t)+2cos(2t)

x^{^{''}} + 4 x = - 5 sin (2 t) + 2 cos (2 t)

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

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

y^{''}+3y^'=8x+5

y^{^{''}} + 3 y^{^{'}} = 8 x + 5