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

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

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(dy)/(dx)+1=2y,y(1)=1

\frac{d y}{d x} + 1 = 2 y, y (1) = 1

y = \frac{e ^{2 x - 2}}{2} + \frac{1}{2}

Solution steps

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

Solve separable ODE:

y = \frac{e ^{2 x - 2}}{2} + \frac{1}{2}

y = \frac{e ^{2 x - 2}}{2} + \frac{1}{2}

\int \frac{2 u - 1}{4 u ^{2} - 1} d u

\int \frac{4 y}{1} d y

y = 2 e^{x} cos (x), (0, 2)

\int x^{π} d x

\int 2 x + 3 d x

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