What is the solution for (x-1)y^'+xy=6e^x ?

The solution for (x-1)y^'+xy=6e^x is y=(3e^x)/(x-1)+(c_{1})/(e^{x-1+c_{1)}x-e^{x-1+c_{1}}}

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(x-1)y^'+xy=6e^x

(x - 1) y^{^{'}} + x y = 6 e^{x}

y = \frac{3 e ^{x}}{x - 1} + \frac{c _{1}}{e ^{x - 1 + c_{1}} x - e ^{x - 1 + c_{1}}}

Solution steps

(x - 1) y^{'} (x) + x y = 6 e^{x}

Solve linear ODE:

y = \frac{3 e ^{x}}{x - 1} + \frac{c _{1}}{e ^{x - 1 + c_{1}} x - e ^{x - 1 + c_{1}}}

y = \frac{3 e ^{x}}{x - 1} + \frac{c _{1}}{e ^{x - 1 + c_{1}} x - e ^{x - 1 + c_{1}}}

n = 1 \sum \infty \frac{n !}{n ^{n}}

\int tan^{3} (x) (sec (x))^{- \frac{1}{2}} d x

\int_{0}^{2} (2 + x) d x

5 e^{x} + x

\int k \cdot x d x

What is the solution for (x-1)y^'+xy=6e^x ?
The solution for (x-1)y^'+xy=6e^x is y=(3e^x)/(x-1)+(c_{1})/(e^{x-1+c_{1)}x-e^{x-1+c_{1}}}