What is the solution for y^'+y=x+sqrt(5) ?

The solution for y^'+y=x+sqrt(5) is y=x-1+sqrt(5)+(c_{1})/(e^x)

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y^'+y=x+sqrt(5)

y^{^{'}} + y = x + 5

y = x - 1 + 5 + \frac{c _{1}}{e ^{x}}

Solution steps

y^{'} (x) + y = x + 5

Solve linear ODE:

y = x - 1 + 5 + \frac{c _{1}}{e ^{x}}

y = x - 1 + 5 + \frac{c _{1}}{e ^{x}}

\int \frac{1}{64 + x ^{2}} d x

\int \frac{( x ^{3} )}{1 + x ^{2}} d x

2 x^{2} + x - 2

\int_{0}^{\infty} \frac{5}{x ^{3}} d x

0 = x^{2} - x y + 2 y - 2, at x = - 2

What is the solution for y^'+y=x+sqrt(5) ?
The solution for y^'+y=x+sqrt(5) is y=x-1+sqrt(5)+(c_{1})/(e^x)