What is the solution for (dx)/(dt)=5000+0.04x,x=18000,t=0 ?

The solution for (dx)/(dt)=5000+0.04x,x=18000,t=0 is x=143000e^{t/(25)}-125000

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(dx)/(dt)=5000+0.04x,x=18000,t=0

\frac{d x}{d t} = 5000 + 0.04 x, x = 18000, t = 0

x = 143000 e^{\frac{t}{25}} - 125000

Solution steps

\frac{d x}{d t} = 5000 + 0.04 x

Solve separable ODE:

x = 143000 e^{\frac{t}{25}} - 125000

x = 143000 e^{\frac{t}{25}} - 125000

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

\frac{d y}{d t} = 3 - 0.04 y

\frac{x y + 3 x - y - 3}{x y - 2 x + 4 y - 8} = \frac{d y}{d x}

(t^{2} - 14 t + 45) \frac{d y}{d t} = y

\frac{d y}{d x} = y^{2} (7 - e^{x})

What is the solution for (dx)/(dt)=5000+0.04x,x=18000,t=0 ?
The solution for (dx)/(dt)=5000+0.04x,x=18000,t=0 is x=143000e^{t/(25)}-125000