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Beliebt Rechnen >

y^{'''}+6y^{''}=x^2

Lösung

y^{^{'''}} + 6 y^{^{''}} = x^{2}

Lösung

y = c_{1} e^{- 6 x} + c_{2} + c_{3} x + \frac{x ^{4}}{72} - \frac{x ^{3}}{108} + \frac{x ^{2}}{216}

Schritte zur Lösung

y^{'''} (x) + 6 y^{''} (x) = x^{2}

Solve linear ODE:

y = c_{1} e^{- 6 x} + c_{2} + c_{3} x + \frac{x ^{4}}{72} - \frac{x ^{3}}{108} + \frac{x ^{2}}{216}

y = c_{1} e^{- 6 x} + c_{2} + c_{3} x + \frac{x ^{4}}{72} - \frac{x ^{3}}{108} + \frac{x ^{2}}{216}

Graph

Beliebte Beispiele

(d^3+4d)y=sin^2(x)

(d^{3} + 4 d) y = sin^{2} (x)

y^{''}+y^'=t^2+2t

y^{^{''}} + y^{^{'}} = t^{2} + 2 t

y^{''}+9y=10,e^{-t}y(0)y^'(0)=0

y^{^{''}} + 9 y = 10, e^{- t} y (0) y^{^{'}} (0) = 0

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

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

y^{''}+y=(cos(x)+1)/(sin(x))

y^{^{''}} + y = \frac{cos ( x ) + 1}{sin ( x )}