I'm doing a work-through of Boyce/DiPrima's EDE (10th Ed), and one of the problems is to solve explicitly the following equation:
y^2*(1-x^2)^(1/2) dy = arcsin[x] dx
Now I was ultimately able to solve it manually. But for grins (or laziness) I initially tried my newly-purchased Mathematica v.10 on it, and couldn't convince "DSolve" to solve it. Clearly I must be doing something wrong, because I've only been playing with my new best friend for a few days, and I'm already convinced he/she is WAY smarter than I am (not that this is any great feat).
Anyway, when couching the 'DSolve' command as follows:
DSolve[y'[x] == (ArcSin[x]/(1 - x^2)^(1/2))/y[x]^2), y[x], x]...
...I get the empty set symbol (ie: {{ }} ...)
If I try to do it implicitly (which I'm not sure DSolve understands):
DSolve[(y[x]^2)*y'[x] == ArcSin[x]/(1 - x^2)^(1/2), y[x], x]...
...I get an error message stating that the given equation is not a differential equation (I'm thus assuming here that DSolve cannot accept input implicitly).
So I'm stumped: the (seeming) 'right' way gets me the wrong answer (ie: I know there is an explicit solution), and I don't seem to be able to input the equation implicitly. Anyone see what I'm doing wrong?
Thanks in advance!