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Beliebt Rechnen >

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

Lösung

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

Lösung

y = c_{1} + c_{2} e^{- 2 x} + \frac{x ^{3}}{6} - \frac{x ^{2}}{4} + \frac{x}{4}

Schritte zur Lösung

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

Solve linear ODE:

y = c_{1} + c_{2} e^{- 2 x} + \frac{x ^{3}}{6} - \frac{x ^{2}}{4} + \frac{x}{4}

y = c_{1} + c_{2} e^{- 2 x} + \frac{x ^{3}}{6} - \frac{x ^{2}}{4} + \frac{x}{4}

Graph

Beliebte Beispiele

y^{''}-4y^'+5y=e^{-3t},y(0)=1,y^'(0)=0

y^{^{''}} - 4 y^{^{'}} + 5 y = e^{- 3 t}, y (0) = 1, y^{^{'}} (0) = 0

(d^2y)/(dx^2)+100y=csc(10x)

\frac{d ^{2} y}{d x ^{2}} + 100 y = csc (10 x)

y^{''}+y^'+y=x^4+4x^3+12x^2

y^{^{''}} + y^{^{'}} + y = x^{4} + 4 x^{3} + 12 x^{2}

(D^2+5D+6)y=(D+1)x

(D^{2} + 5 D + 6) y = (D + 1) x

y^{''}+4y^'=2sec^3(2t)

y^{^{''}} + 4 y^{^{'}} = 2 sec^{3} (2 t)