What is the solution for y^'+3y=cos(x) ?

The solution for y^'+3y=cos(x) is y=(sin(x))/(10)+(3cos(x))/(10)+(c_{1})/(e^{3x)}

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y^'+3y=cos(x)

y^{^{'}} + 3 y = cos (x)

y = \frac{sin ( x )}{10} + \frac{3 cos ( x )}{10} + \frac{c _{1}}{e ^{3 x}}

Solution steps

y^{'} (x) + 3 y = cos (x)

Solve linear ODE:

y = \frac{sin ( x )}{10} + \frac{3 cos ( x )}{10} + \frac{c _{1}}{e ^{3 x}}

y = \frac{sin ( x )}{10} + \frac{3 cos ( x )}{10} + \frac{c _{1}}{e ^{3 x}}

4 y^{^{''}} + y^{^{'}} + 8 y = 0

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

x \to 5 lim (5 + x^{4})

\int e^{- s t} (t) d t

\int \frac{x ^{\frac{3}{2}} + 2 x ^{6} + 1.2}{x} d x

What is the solution for y^'+3y=cos(x) ?
The solution for y^'+3y=cos(x) is y=(sin(x))/(10)+(3cos(x))/(10)+(c_{1})/(e^{3x)}