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

Lösung

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

y = c_{1} cos (2 x) + c_{2} sin (2 x) - \frac{x ^{3} cos ( 2 x )}{12} + \frac{x ^{2} sin ( 2 x )}{16} + \frac{x cos ( 2 x )}{32}

Schritte zur Lösung

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

Solve linear ODE:

y = c_{1} cos (2 x) + c_{2} sin (2 x) - \frac{x ^{3} cos ( 2 x )}{12} + \frac{x ^{2} sin ( 2 x )}{16} + \frac{x cos ( 2 x )}{32}

y = c_{1} cos (2 x) + c_{2} sin (2 x) - \frac{x ^{3} cos ( 2 x )}{12} + \frac{x ^{2} sin ( 2 x )}{16} + \frac{x cos ( 2 x )}{32}

y^{^{''}} + 4 y^{^{'}} + 4 y = \frac{e ^{- 2} x}{x ^{3}}

x^{^{'''}} - x = 3 e^{t}

y^{^{'''}} + y^{^{'}} + 2 = 0

(d^{3} - d^{2} - 6 d) y = x^{2} + 1

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