Solve for s: Differential Equation with Initial Condition s(0)=20,000

[georg gill]

$$\frac{ds}{dt}=600-\frac{2s}{200+t}$$

$$\frac{ds}{dt}+\frac{2s}{200+t}=600$$

$$\frac{ds}{dt}e^{ln(100+t/2)}+\frac{2s}{200+t}e^{ln(100+t/2)}=e^{ln(100+t/2)}600$$

$$\frac{d}{dt}(se^{ln(100+t/2)})=(100+t/2)600$$

$$se^{ln(100+t/2)}=\int(100+t/2)600dt$$

$$s(100+t/2)=600(100t+t^2/4)+C$$

t=0 s=20 000

$$20.000\cdot100=C$$

But this is wrong

I guess i want to know what I did wrong. I used the product rule for derivation backwards. Here is answer sheet

http://bildr.no/view/1051423

 

[dextercioby]

The integrating factor is wrong. Revise your calculation and look up the formula for it in the book.