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

Lösung

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

y = c_{1} cos (2 x) + c_{2} sin (2 x) + \frac{1}{2} ln (cos^{2} (x)) cos (2 x) + (- \frac{1}{2} tan (x) + x) sin (2 x)

Schritte zur Lösung

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

Solve linear ODE:

y = c_{1} cos (2 x) + c_{2} sin (2 x) + \frac{1}{2} ln (cos^{2} (x)) cos (2 x) + (- \frac{1}{2} tan (x) + x) sin (2 x)

y = c_{1} cos (2 x) + c_{2} sin (2 x) + \frac{1}{2} ln (cos^{2} (x)) cos (2 x) + (- \frac{1}{2} tan (x) + x) sin (2 x)

y^{^{''}} + 2 y^{^{'}} - 3 y = 1, y (0) = e^{x} - \frac{1}{3}

y^{^{'''}} - 12 y^{^{''}} + 256 y = e^{8 x}

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

\frac{1}{2} x^{^{''}} + \frac{1}{2} x^{^{'}} + 6 x = 10 cos (3 t)

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