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Beliebt Rechnen >

(D^4+4D^2)y=sin(2x)+xe^x+4

Lösung

(D^{4} + 4 D^{2}) y = sin (2 x) + x e^{x} + 4

Lösung

y = c_{1} + c_{2} x + c_{3} cos (2 x) + c_{4} sin (2 x) + \frac{x cos ( 2 x )}{16} + \frac{e ^{x} x}{5} - \frac{12}{25} e^{x} + \frac{x ^{2}}{2}

Schritte zur Lösung

(D^{4} + 4 D^{2}) y = sin (2 x) + x e^{x} + 4

Solve linear ODE:

y = c_{1} + c_{2} x + c_{3} cos (2 x) + c_{4} sin (2 x) + \frac{x cos ( 2 x )}{16} + \frac{e ^{x} x}{5} - \frac{12}{25} e^{x} + \frac{x ^{2}}{2}

y = c_{1} + c_{2} x + c_{3} cos (2 x) + c_{4} sin (2 x) + \frac{x cos ( 2 x )}{16} + \frac{e ^{x} x}{5} - \frac{12}{25} e^{x} + \frac{x ^{2}}{2}

Graph

Beliebte Beispiele

y^{''}+5(dy)/(dx)-6y=2+(-2)sin(2x)

y^{^{''}} + 5 \frac{d y}{d x} - 6 y = 2 + (- 2) sin (2 x)

y^{''}+2y^'-3y=e^{-3t},y(0)=0,y^'(0)=0

y^{^{''}} + 2 y^{^{'}} - 3 y = e^{- 3 t}, y (0) = 0, y^{^{'}} (0) = 0

x^{^{''}} + x = 4 e^{t}

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

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

D u = 50 - \frac{1}{500}