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Beliebt Rechnen >

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

Lösung

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

Lösung

y = c_{1} e^{- x} + c_{2} e^{- 2 x} + \frac{x ^{2}}{2} - \frac{x}{2} + \frac{1}{4}

Schritte zur Lösung

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

Solve linear ODE:

y = c_{1} e^{- x} + c_{2} e^{- 2 x} + \frac{x ^{2}}{2} - \frac{x}{2} + \frac{1}{4}

y = c_{1} e^{- x} + c_{2} e^{- 2 x} + \frac{x ^{2}}{2} - \frac{x}{2} + \frac{1}{4}

Graph

Beliebte Beispiele

y^{''}-a^2*y+b=0

y^{^{''}} - a^{2} \cdot y + b = 0

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

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

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

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

(d^2y)/(dx^2)+10(dy)/(dx)+16y=40cos(x)

\frac{d ^{2} y}{d x ^{2}} + 10 \frac{d y}{d x} + 16 y = 40 cos (x)

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

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