(d^4+d^3+d^2)y=5x^2+cos(x)

Lösung

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

y = c_{1} + c_{2} x + e^{- \frac{x}{2}} (c_{3} cos (\frac{3 x}{2}) + c_{4} sin (\frac{3 x}{2})) + \frac{5 x ^{4}}{12} - \frac{5 x ^{3}}{3} - sin (x)

Schritte zur Lösung

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

Solve linear ODE:

y = c_{1} + c_{2} x + e^{- \frac{x}{2}} (c_{3} cos (\frac{3 x}{2}) + c_{4} sin (\frac{3 x}{2})) + \frac{5 x ^{4}}{12} - \frac{5 x ^{3}}{3} - sin (x)

y = c_{1} + c_{2} x + e^{- \frac{x}{2}} (c_{3} cos (\frac{3 x}{2}) + c_{4} sin (\frac{3 x}{2})) + \frac{5 x ^{4}}{12} - \frac{5 x ^{3}}{3} - sin (x)

(d^{4} + d^{3} + d^{2}) y = 5 x^{2}

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

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

(d - 1)^{2} y = 2 lo g_{10} (x)

y^{^{'''}} - y^{^{''}} = 12 x^{2} + 6 x