3y^{''}-5y^'+y=x^2+1+sin(2x)

Lösung

3 y^{^{''}} - 5 y^{^{'}} + y = x^{2} + 1 + sin (2 x)

y = c_{1} e^{\frac{( 5 + 13 ) x}{6}} + c_{2} e^{\frac{( 5 - 13 ) x}{6}} + x^{2} + 10 x + 45 - \frac{11}{221} sin (2 x) + \frac{10}{221} cos (2 x)

Schritte zur Lösung

3 y^{''} (x) - 5 y^{'} (x) + y = x^{2} + 1 + sin (2 x)

Solve linear ODE:

y = c_{1} e^{\frac{( 5 + 13 ) x}{6}} + c_{2} e^{\frac{( 5 - 13 ) x}{6}} + x^{2} + 10 x + 45 - \frac{11}{221} sin (2 x) + \frac{10}{221} cos (2 x)

y = c_{1} e^{\frac{( 5 + 13 ) x}{6}} + c_{2} e^{\frac{( 5 - 13 ) x}{6}} + x^{2} + 10 x + 45 - \frac{11}{221} sin (2 x) + \frac{10}{221} cos (2 x)

y^{^{''}} - y^{^{'}} - 6 y = 6 cos (3 x)

y^{^{''}} - 6 y + y^{^{'}} = e^{x}

y^{^{''}} - 4 y = - 12 sin (2 t)

\frac{d ^{2} y}{d x ^{2}} - 5 \frac{d y}{d x} + 4 y = tan (x)

y^{^{''}} + y = 2 e^{t}