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

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

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

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

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

Solution steps

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

Solve separable ODE:

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

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

y^{^{'}} + 2 x y = 3 x

\frac{d y}{d x} = x^{4} (y - 3), y (0) = 9

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

\frac{d y}{d x} = - \frac{8}{4} x^{3} y^{5}

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

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