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Beliebt Rechnen >

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

Lösung

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

Lösung

y = c_{1} e^{2 x} + c_{2} e^{- 2 x} + c_{3} + c_{4} x - \frac{x ^{4}}{48} - \frac{x ^{2}}{16} - \frac{1}{3} e^{x}

Schritte zur Lösung

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

Solve linear ODE:

y = c_{1} e^{2 x} + c_{2} e^{- 2 x} + c_{3} + c_{4} x - \frac{x ^{4}}{48} - \frac{x ^{2}}{16} - \frac{1}{3} e^{x}

y = c_{1} e^{2 x} + c_{2} e^{- 2 x} + c_{3} + c_{4} x - \frac{x ^{4}}{48} - \frac{x ^{2}}{16} - \frac{1}{3} e^{x}

Graph

Beliebte Beispiele

y^{''}+9y=5sin(2x),y(0)=1,y^'(0)=0

y^{^{''}} + 9 y = 5 sin (2 x), y (0) = 1, y^{^{'}} (0) = 0

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

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

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

y^{''}-9y=-8e^t

y^{^{''}} - 9 y = - 8 e^{t}

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

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