y^{''}+5y^'+4y=8x^2+3+2cos^2(x)

Lösung

y^{^{''}} + 5 y^{^{'}} + 4 y = 8 x^{2} + 3 + 2 cos^{2} (x)

y = c_{1} e^{- x} + c_{2} e^{- 4 x} + \frac{120 x ^{2} - 300 x + 40 cos ^{2} ( x ) + 6 sin ( 2 x ) - 20 cos ( 2 x ) + 355}{60}

Schritte zur Lösung

y^{''} (x) + 5 y^{'} (x) + 4 y = 8 x^{2} + 3 + 2 cos^{2} (x)

Solve linear ODE:

y = c_{1} e^{- x} + c_{2} e^{- 4 x} + \frac{120 x ^{2} - 300 x + 40 cos ^{2} ( x ) + 6 sin ( 2 x ) - 20 cos ( 2 x ) + 355}{60}

y = c_{1} e^{- x} + c_{2} e^{- 4 x} + \frac{120 x ^{2} - 300 x + 40 cos ^{2} ( x ) + 6 sin ( 2 x ) - 20 cos ( 2 x ) + 355}{60}

y^{^{''}} - 3 y^{^{'}} + 10 y = cosh (2 x)

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

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

y^{^{''}} + 4 y = 0, y^{1} (0) = sin^{2} (x)

2 y^{^{''}} - 72 y = 0