What is the solution for y^'=0.05y-k,y(0)=400000,y(15)=0 ?

The solution for y^'=0.05y-k,y(0)=400000,y(15)=0 is y=400000e^{t/(20)}-20ke^{t/(20)}+20k

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y^'=0.05y-k,y(0)=400000,y(15)=0

y^{^{'}} = 0.05 y - k, y (0) = 400000, y (15) = 0

y = 400000 e^{\frac{t}{20}} - 20 k e^{\frac{t}{20}} + 20 k

Solution steps

y^{'} (t) = 0.05 y - k

Solve separable ODE:

y = 400000 e^{\frac{t}{20}} - 20 k e^{\frac{t}{20}} + 20 k

y = 400000 e^{\frac{t}{20}} - 20 k e^{\frac{t}{20}} + 20 k

\frac{d y}{d x} = 5 x y, y = 0

x = \frac{y}{y ^{^{'}}}

d y \cdot x = 3 y \cdot d x

\frac{d x}{d t} = 10 - 0.6 x

u^{^{'}} = 3 e^{7 x - H (x)}

What is the solution for y^'=0.05y-k,y(0)=400000,y(15)=0 ?
The solution for y^'=0.05y-k,y(0)=400000,y(15)=0 is y=400000e^{t/(20)}-20ke^{t/(20)}+20k