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Beliebt Rechnen >

(d^2+1)y=e^{-x}+cos(x)+x^3+e^xcos(x)

Lösung

(d^{2} + 1) \cdot y = e^{- x} + cos (x) + x^{3} + e^{x} \cdot cos (x)

Lösung

y = c_{1} cos (x) + c_{2} sin (x) + \frac{1}{2} e^{- x} + \frac{x sin ( x )}{2} + x^{3} - 6 x + \frac{2}{5} e^{x} sin (x) + \frac{1}{5} e^{x} cos (x)

Schritte zur Lösung

(d^{2} + 1) y = e^{- x} + cos (x) + x^{3} + e^{x} cos (x)

Solve linear ODE:

y = c_{1} cos (x) + c_{2} sin (x) + \frac{1}{2} e^{- x} + \frac{x sin ( x )}{2} + x^{3} - 6 x + \frac{2}{5} e^{x} sin (x) + \frac{1}{5} e^{x} cos (x)

y = c_{1} cos (x) + c_{2} sin (x) + \frac{1}{2} e^{- x} + \frac{x sin ( x )}{2} + x^{3} - 6 x + \frac{2}{5} e^{x} sin (x) + \frac{1}{5} e^{x} cos (x)

Graph

Beliebte Beispiele

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

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

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

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

(d^2+1)y=sin(x)sin^2(x)

(d^{2} + 1) y = sin (x) sin^{2} (x)

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

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

y^{''}+y=sec(x^3)

y^{^{''}} + y = sec (x^{3})