Question

find the one-parameter family of solutions for (1+x^2)dy/dx=y

Answer 1

=> dx/(1+x^2) = dy/y

integrate both sides..

Answer 2

what do I do next?

Answer 3

integrate ,.thats the only thing you require to do ..

Answer 4

i mean,integrate both sides..

Answer 5

I integrated both sides. There's nothing else to do? I get arctanx+c=lny+c

Answer 6

you may treat sum or difference of both constants as another constant C..

so i guess ans would be

arctanx = lny + C

Answer 7

or you may want to solve for y from here..

Answer 8

for that,,let C = log k ,,where k = another constant

=> arctan x = lny + ln k
=> arctan x = ln(yk)
=>e^(arctan x) /k = y

or y = Ke^(arctan (x))

Answer 9

where K=1/k ..

Answer 10

thank shubham!

Answer 11

your welcome,,glad to help..