(d^3-4d)y=2cosh^2(2x)

Lösung

(d^{3} - 4 d) y = 2 cosh^{2} (2 x)

y = c_{1} + c_{2} e^{- 2 x} + c_{3} e^{2 x} - \frac{1}{4} (x + \frac{1}{4} sinh (4 x)) + e^{- 2 x} \cdot \int \frac{e ^{2 x} cosh ^{2} ( 2 x )}{4} d x + e^{2 x} \cdot \int \frac{e ^{- 2 x} cosh ^{2} ( 2 x )}{4} d x

Schritte zur Lösung

(d^{3} - 4 d) y = 2 cosh^{2} (2 x)

Solve linear ODE:

y = c_{1} + c_{2} e^{- 2 x} + c_{3} e^{2 x} - \frac{1}{4} (x + \frac{1}{4} sinh (4 x)) + e^{- 2 x} \cdot \int \frac{e ^{2 x} cosh ^{2} ( 2 x )}{4} d x + e^{2 x} \cdot \int \frac{e ^{- 2 x} cosh ^{2} ( 2 x )}{4} d x

y = c_{1} + c_{2} e^{- 2 x} + c_{3} e^{2 x} - \frac{1}{4} (x + \frac{1}{4} sinh (4 x)) + e^{- 2 x} \cdot \int \frac{e ^{2 x} cosh ^{2} ( 2 x )}{4} d x + e^{2 x} \cdot \int \frac{e ^{- 2 x} cosh ^{2} ( 2 x )}{4} d x

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

(d^{2} - 4) y = x^{2}

y^{^{''}} - y = e^{x} + 1

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

y^{^{''}} + 16 y = 32 sec (2 x)