What is the solution for y^'=0.01y-100,y(0)=20000 ?

The solution for y^'=0.01y-100,y(0)=20000 is y=10000e^{t/(100)}+10000

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y^'=0.01y-100,y(0)=20000

y^{^{'}} = 0.01 y - 100, y (0) = 20000

y = 10000 e^{\frac{t}{100}} + 10000

Solution steps

y^{'} (t) = 0.01 y - 100

Solve separable ODE:

y = 10000 e^{\frac{t}{100}} + 10000

y = 10000 e^{\frac{t}{100}} + 10000

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

x y^{^{'}} - y = x y

y^{^{'}} = 7 sin (7 x) y

\frac{y ^{^{'}} - ( y )}{( x + y ^{2} )} = 0

(x^{4} + 5 x^{4} y^{2}) d x + e^{x^{5}} y d y = 0

What is the solution for y^'=0.01y-100,y(0)=20000 ?
The solution for y^'=0.01y-100,y(0)=20000 is y=10000e^{t/(100)}+10000