y^{''}-2y^'+y=(e^t)/((1+t^2)+3e^t)

Lösung

y^{^{''}} - 2 y^{^{'}} + y = \frac{e ^{t}}{( 1 + t ^{2} ) + 3 e ^{t}}

y = c_{1} e^{t} + c_{2} t e^{t} + e^{t} \cdot \int - \frac{t}{1 + t ^{2} + 3 e ^{t}} d t + e^{t} t \cdot \int \frac{1}{1 + t ^{2} + 3 e ^{t}} d t

Schritte zur Lösung

y^{''} (t) - 2 y^{'} (t) + y = \frac{e ^{t}}{( 1 + t ^{2} ) + 3 e ^{t}}

Solve linear ODE:

y = c_{1} e^{t} + c_{2} t e^{t} + e^{t} \cdot \int - \frac{t}{1 + t ^{2} + 3 e ^{t}} d t + e^{t} t \cdot \int \frac{1}{1 + t ^{2} + 3 e ^{t}} d t

y = c_{1} e^{t} + c_{2} t e^{t} + e^{t} \cdot \int - \frac{t}{1 + t ^{2} + 3 e ^{t}} d t + e^{t} t \cdot \int \frac{1}{1 + t ^{2} + 3 e ^{t}} d t

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

y^{^{''}} + 2 y^{^{'}} + 2 y = 4 cos (t) + 2 sin (t)

y^{^{''}} + 10 y^{^{'}} + 25 y = 100 sinh (5 x)

y^{^{''}} + 2 y^{^{'}} + y = 9 e^{- t}

y^{^{''}} - y = x^{3} - x