y^{''}+9y=2x^2e^{3x}+5

Lösung

y^{^{''}} + 9 y = 2 x^{2} e^{3 x} + 5

y = c_{1} cos (3 x) + c_{2} sin (3 x) + \frac{e ^{3 x} x ^{2} + 5}{9} - \frac{2 e ^{3 x} x}{27} + \frac{1}{81} e^{3 x}

Schritte zur Lösung

y^{''} (x) + 9 y = 2 x^{2} e^{3 x} + 5

Solve linear ODE:

y = c_{1} cos (3 x) + c_{2} sin (3 x) + \frac{e ^{3 x} x ^{2} + 5}{9} - \frac{2 e ^{3 x} x}{27} + \frac{1}{81} e^{3 x}

y = c_{1} cos (3 x) + c_{2} sin (3 x) + \frac{e ^{3 x} x ^{2} + 5}{9} - \frac{2 e ^{3 x} x}{27} + \frac{1}{81} e^{3 x}

y^{^{''}} - y^{^{'}} - 12 y = - 5 e^{3 x}, y (0) = 0, y^{^{'}} (0) = 0

x^{^{''}} + 16 x^{^{'}} = 144, x (0) = 5, x^{^{'}} (0) = 12

y^{^{''}} - 90 y = sin (2 x)

y^{^{''}} + 25 \cdot y = \frac{1}{sin ( 5 \cdot x )}

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