(d^6-d^4)y=x^2

Lösung

(d^{6} - d^{4}) y = x^{2}

y = c_{1} e^{x} + c_{2} e^{- x} + c_{3} + c_{4} x + c_{5} x^{2} + c_{6} x^{3} - x^{2} + \frac{- x ^{6} - 30 x ^{4}}{360} - 2

Schritte zur Lösung

(d^{6} - d^{4}) y = x^{2}

Solve linear ODE:

y = c_{1} e^{x} + c_{2} e^{- x} + c_{3} + c_{4} x + c_{5} x^{2} + c_{6} x^{3} - x^{2} + \frac{- x ^{6} - 30 x ^{4}}{360} - 2

y = c_{1} e^{x} + c_{2} e^{- x} + c_{3} + c_{4} x + c_{5} x^{2} + c_{6} x^{3} - x^{2} + \frac{- x ^{6} - 30 x ^{4}}{360} - 2

y^{2} - 5 x + 6 = 0

3 x^{2} - 2 y = 5

2 x^{2} - 9 y + 6 x - 3 y^{2} = 1

y^{2} = x^{2} + 6

4 x^{2} - 3 y^{2} - 8 x - 8 = 0