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Beliebt Rechnen >

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

Lösung

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

Lösung

y = c_{1} + c_{2} e^{- x} + c_{3} e^{x} - \frac{x ^{3}}{3} + \frac{1}{2} e^{x} x^{2} - \frac{3}{2} e^{x} x - 2 x + \frac{7}{4} e^{x} + \frac{1}{6} e^{2 x}

Schritte zur Lösung

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

Solve linear ODE:

y = c_{1} + c_{2} e^{- x} + c_{3} e^{x} - \frac{x ^{3}}{3} + \frac{1}{2} e^{x} x^{2} - \frac{3}{2} e^{x} x - 2 x + \frac{7}{4} e^{x} + \frac{1}{6} e^{2 x}

y = c_{1} + c_{2} e^{- x} + c_{3} e^{x} - \frac{x ^{3}}{3} + \frac{1}{2} e^{x} x^{2} - \frac{3}{2} e^{x} x - 2 x + \frac{7}{4} e^{x} + \frac{1}{6} e^{2 x}

Graph

Beliebte Beispiele

4y^{''}+16y=sin(x)+2cos(x)

4 y^{^{''}} + 16 y = sin (x) + 2 cos (x)

y^{''}+y=xsin(x),y(0)=1,y^'(0)=0

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

y^{'''}-2y^{''}-y^'+2y=-8ex+6e-x

y^{^{'''}} - 2 y^{^{''}} - y^{^{'}} + 2 y = - 8 e x + 6 e - x

y^{''}+16y=csc(4x)

y^{^{''}} + 16 y = csc (4 x)

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

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