4y^{''}+4y=2sec(t/2)

Lösung

4 y^{^{''}} + 4 y = 2 sec (\frac{t}{2})

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

Schritte zur Lösung

4 y^{''} (t) + 4 y = 2 sec (\frac{t}{2})

Solve linear ODE:

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

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

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

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

y^{^{''}} + 2 y^{^{'}} + y = x^{2} + 3 x

y^{^{''}} + y = sec (x^{3})

y^{^{''}} - y^{^{'}} = \frac{e ^{2} x}{( 2 + e ^{x} )}