- #1
vladimir69
- 130
- 0
just a couple of questions:
given dy/dx=sqrt(x^2+y^2-9)
and y(a)=b
i)for what values of a and b would a local solution exist and why
ii)for what values of a and b would a unique solution exist and why
for i) i got all values such that a^2+b^2<=9
for ii) i got all values such that a^2+b^2>9
i'm not 100% sure this is correct and would be happy if someone could confirm/show otherwise these results.
secondly
how would one show that the only solution of
y''+ty'+(1+t^2)y^2=0
that touches the t axis at some point (t0,0) is the identically zero solution
thanks for your help
given dy/dx=sqrt(x^2+y^2-9)
and y(a)=b
i)for what values of a and b would a local solution exist and why
ii)for what values of a and b would a unique solution exist and why
for i) i got all values such that a^2+b^2<=9
for ii) i got all values such that a^2+b^2>9
i'm not 100% sure this is correct and would be happy if someone could confirm/show otherwise these results.
secondly
how would one show that the only solution of
y''+ty'+(1+t^2)y^2=0
that touches the t axis at some point (t0,0) is the identically zero solution
thanks for your help