What is the solution for 2(d^2y)/(dx^2)+2(dy)/(dx)+y=1 ?

The solution for 2(d^2y)/(dx^2)+2(dy)/(dx)+y=1 is y=e^{-x/2}(c_{1}cos(x/2)+c_{2}sin(x/2))+1

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2(d^2y)/(dx^2)+2(dy)/(dx)+y=1

2 \frac{d ^{2} y}{d x ^{2}} + 2 \frac{d y}{d x} + y = 1

y = e^{- \frac{x}{2}} (c_{1} cos (\frac{x}{2}) + c_{2} sin (\frac{x}{2})) + 1

Solution steps

2 \frac{d ^{2} y}{d x ^{2}} + 2 \frac{d y}{d x} + y = 1

Solve linear ODE:

y = e^{- \frac{x}{2}} (c_{1} cos (\frac{x}{2}) + c_{2} sin (\frac{x}{2})) + 1

y = e^{- \frac{x}{2}} (c_{1} cos (\frac{x}{2}) + c_{2} sin (\frac{x}{2})) + 1

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

3 x^{\frac{4}{3}} - 2 x^{\frac{1}{7}}

x \to - 3 lim (\frac{( x ^{2} + 7 x + 12 )}{x ^{2} - 9})

x \to 3 lim (\frac{x ^{2} - 9}{x + 1})

\int 4 cos (6 x) d x

What is the solution for 2(d^2y)/(dx^2)+2(dy)/(dx)+y=1 ?
The solution for 2(d^2y)/(dx^2)+2(dy)/(dx)+y=1 is y=e^{-x/2}(c_{1}cos(x/2)+c_{2}sin(x/2))+1