y^{''}-y^'+2y=6e^{1/2}

Lösung

y^{^{''}} - y^{^{'}} + 2 y = 6 e^{\frac{1}{2}}

y = e^{\frac{t}{2}} (c_{1} cos (\frac{7 ^{\frac{1}{2}} t}{2}) + c_{2} sin (\frac{7 ^{\frac{1}{2}} t}{2})) + 3 e^{\frac{1}{2}}

Schritte zur Lösung

y^{''} (t) - y^{'} (t) + 2 y = 6 e^{\frac{1}{2}}

Solve linear ODE:

y = e^{\frac{t}{2}} (c_{1} cos (\frac{7 ^{\frac{1}{2}} t}{2}) + c_{2} sin (\frac{7 ^{\frac{1}{2}} t}{2})) + 3 e^{\frac{1}{2}}

y = e^{\frac{t}{2}} (c_{1} cos (\frac{7 ^{\frac{1}{2}} t}{2}) + c_{2} sin (\frac{7 ^{\frac{1}{2}} t}{2})) + 3 e^{\frac{1}{2}}

y^{^{''}} + 16 y = 2 csc^{2} (4 x)

y^{^{''}} + 5 y^{^{'}} + 6 y = sin (x) - cos (2 x)

y^{^{''}} - 10 y^{^{'}} + 25 = e^{5 x} ln (4 + x^{2})

y^{^{''}} + y = 4 x^{2}

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