(d^2+3d+2)y=4cos^2(x)

Lösung

(d^{2} + 3 d + 2) y = 4 cos^{2} (x)

y = c_{1} e^{- x} + c_{2} e^{- 2 x} - \frac{11}{10} cos (2 x) + \frac{3}{10} sin (2 x) + 2 cos^{2} (x)

Schritte zur Lösung

(d^{2} + 3 d + 2) y = 4 cos^{2} (x)

Solve linear ODE:

y = c_{1} e^{- x} + c_{2} e^{- 2 x} - \frac{11}{10} cos (2 x) + \frac{3}{10} sin (2 x) + 2 cos^{2} (x)

y = c_{1} e^{- x} + c_{2} e^{- 2 x} - \frac{11}{10} cos (2 x) + \frac{3}{10} sin (2 x) + 2 cos^{2} (x)

y^{^{''}} + 3 y^{^{'}} = - 48 x^{2} e^{3} x

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

(d^{3} + 4 d) y = 4 cot (2 x)

d (x) = 243 e^{- 0} 0.1 x

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