What is the solution for x^'+2/(1+t)x=(e^t)/(1+t) ?

The solution for x^'+2/(1+t)x=(e^t)/(1+t) is x=(e^tt)/(1+2t+t^2)+(c_{1})/(1+2t+t^2)

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x^'+2/(1+t)x=(e^t)/(1+t)

x^{^{'}} + \frac{2}{1 + t} x = \frac{e ^{t}}{1 + t}

x = \frac{e ^{t} t}{1 + 2 t + t ^{2}} + \frac{c _{1}}{1 + 2 t + t ^{2}}

Solution steps

x^{'} (t) + \frac{2}{1 + t} x = \frac{e ^{t}}{1 + t}

Solve linear ODE:

x = \frac{e ^{t} t}{1 + 2 t + t ^{2}} + \frac{c _{1}}{1 + 2 t + t ^{2}}

x = \frac{e ^{t} t}{1 + 2 t + t ^{2}} + \frac{c _{1}}{1 + 2 t + t ^{2}}

\int_{- 1}^{1} 3 x^{2} x^{3} + 5 d x

(x^{2} + 2 x)^{^{'}}

x \to 1 + lim (\frac{5}{x ^{3} - 1})

\int \frac{x + 5}{x ^{2} + 10 x} d x

\int_{0}^{1} π (1 - x^{2}) d x

What is the solution for x^'+2/(1+t)x=(e^t)/(1+t) ?
The solution for x^'+2/(1+t)x=(e^t)/(1+t) is x=(e^tt)/(1+2t+t^2)+(c_{1})/(1+2t+t^2)