What is the solution for (dy)/(dx)+(9y)/(1000+x)=0.405 ?

The solution for (dy)/(dx)+(9y)/(1000+x)=0.405 is

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(dy)/(dx)+(9y)/(1000+x)=0.405

\frac{d y}{d x} + \frac{9 y}{1000 + x} = 0.405

y = \frac{0.405 ( 1.0 E 27 x + 4.5 E 24 x ^{2} + 1.2 E 22 x ^{3} + 2.1 E 19 x ^{4} + 2.52 E 16 x ^{5} + 2.1 E 13 x ^{6} + 12000000000 x ^{7} + 4500000 x ^{8} + 1000 x ^{9} + 0.1 x ^{10} )}{100 0 ^{9} + 100 0 ^{8} \cdot 9 x + 100 0 ^{7} \cdot 36 x ^{2} + 100 0 ^{6} \cdot 84 x ^{3} + 100 0 ^{5} \cdot 126 x ^{4} + 100 0 ^{4} \cdot 126 x ^{5} + 84000000000 x ^{6} + 36000000 x ^{7} + 9000 x ^{8} + x ^{9}} + \frac{c _{1}}{100 0 ^{9} + 100 0 ^{8} \cdot 9 x + 100 0 ^{7} \cdot 36 x ^{2} + 100 0 ^{6} \cdot 84 x ^{3} + 100 0 ^{5} \cdot 126 x ^{4} + 100 0 ^{4} \cdot 126 x ^{5} + 84000000000 x ^{6} + 36000000 x ^{7} + 9000 x ^{8} + x ^{9}}

Solution steps

\frac{d y}{d x} + \frac{9 y}{1000 + x} = 0.405

Solve linear ODE:

y = \frac{0.405 ( 1.0 E 27 x + 4.5 E 24 x ^{2} + 1.2 E 22 x ^{3} + 2.1 E 19 x ^{4} + 2.52 E 16 x ^{5} + 2.1 E 13 x ^{6} + 12000000000 x ^{7} + 4500000 x ^{8} + 1000 x ^{9} + 0.1 x ^{10} )}{100 0 ^{9} + 100 0 ^{8} \cdot 9 x + 100 0 ^{7} \cdot 36 x ^{2} + 100 0 ^{6} \cdot 84 x ^{3} + 100 0 ^{5} \cdot 126 x ^{4} + 100 0 ^{4} \cdot 126 x ^{5} + 84000000000 x ^{6} + 36000000 x ^{7} + 9000 x ^{8} + x ^{9}} + \frac{c _{1}}{100 0 ^{9} + 100 0 ^{8} \cdot 9 x + 100 0 ^{7} \cdot 36 x ^{2} + 100 0 ^{6} \cdot 84 x ^{3} + 100 0 ^{5} \cdot 126 x ^{4} + 100 0 ^{4} \cdot 126 x ^{5} + 84000000000 x ^{6} + 36000000 x ^{7} + 9000 x ^{8} + x ^{9}}

y = \frac{0.405 ( 1.0 E 27 x + 4.5 E 24 x ^{2} + 1.2 E 22 x ^{3} + 2.1 E 19 x ^{4} + 2.52 E 16 x ^{5} + 2.1 E 13 x ^{6} + 12000000000 x ^{7} + 4500000 x ^{8} + 1000 x ^{9} + 0.1 x ^{10} )}{100 0 ^{9} + 100 0 ^{8} \cdot 9 x + 100 0 ^{7} \cdot 36 x ^{2} + 100 0 ^{6} \cdot 84 x ^{3} + 100 0 ^{5} \cdot 126 x ^{4} + 100 0 ^{4} \cdot 126 x ^{5} + 84000000000 x ^{6} + 36000000 x ^{7} + 9000 x ^{8} + x ^{9}} + \frac{c _{1}}{100 0 ^{9} + 100 0 ^{8} \cdot 9 x + 100 0 ^{7} \cdot 36 x ^{2} + 100 0 ^{6} \cdot 84 x ^{3} + 100 0 ^{5} \cdot 126 x ^{4} + 100 0 ^{4} \cdot 126 x ^{5} + 84000000000 x ^{6} + 36000000 x ^{7} + 9000 x ^{8} + x ^{9}}

What is the solution for (dy)/(dx)+(9y)/(1000+x)=0.405 ?
The solution for (dy)/(dx)+(9y)/(1000+x)=0.405 is