What is the solution for (dy)/(dx)=0.02y+40000,y(0)=2000000 ?

The solution for (dy)/(dx)=0.02y+40000,y(0)=2000000 is y=4000000e^{x/(50)}-2000000

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(dy)/(dx)=0.02y+40000,y(0)=2000000

\frac{d y}{d x} = 0.02 y + 40000, y (0) = 2000000

y = 4000000 e^{\frac{x}{50}} - 2000000

Solution steps

\frac{d y}{d x} = 0.02 y + 40000

Solve separable ODE:

y = 4000000 e^{\frac{x}{50}} - 2000000

y = 4000000 e^{\frac{x}{50}} - 2000000

y (25 - x^{2})^{\frac{1}{2}} d y = (25 + y^{2})^{\frac{1}{2}} d x

d y = 2 x y e^{x^{2}} d x

\frac{d y}{d x} = y (x^{2} + 6)

(1 - y^{2}) d x + x d y = 0

\frac{d y}{d x} - 2 x y = 2 x, y (0) = 3

What is the solution for (dy)/(dx)=0.02y+40000,y(0)=2000000 ?
The solution for (dy)/(dx)=0.02y+40000,y(0)=2000000 is y=4000000e^{x/(50)}-2000000