dy/dx=x^2+y^2; y(0)=0(adsbygoogle = window.adsbygoogle || []).push({});

okay i solved this question using homogenous

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

subsitute v=y/x

v+x*dv/dx=1+v^2 then use exact equation

dv/(v^2-v+1)=dx/x

dv/((v-1/2)^2+3/4)=(dx/x or just ln(x))

then integrate dv/((v-1/2)^2+3/4)

u=v-1/2

du=dv

dv/(u^2)+3/4

s=2u/sqrt(3)

ds=2/sqrt(3)du

thus

2/sqrt[3]*arctan=ln[x]

then substitue everything back in

2/sqrt[3]*arctan[2u/sqrt[3]]=ln[x]+c

2/sqrt[3]*arctan[2(v-1/2)/sqrt[3]]=ln[x]+c

2/sqrt[3]*arctan[2(y/x-1/2)/sqrt[3]]=ln[x]+c

okay ths thing is now i can not plug in y(0)=0 to get the constant for c and the other thing is this is suppose to be a unique and exisit throughout the interval [0,1/2] i used picard's theorem to show that its continus and estimated h=[0,1/2] the thing is im suppose to plug in 1/2 into y

y(1/2) and when i solve the equation however i can't get a constant

and when i use picard's iteration method successful approximation i do not get the same number. well one thing is i don't have the constant c unless i did the ODE totally wrong. can't think of another first order technique.

when i do picard's iteration method i get .047**** but if i have c i could might have the same answer when i plug in 1/2 one question is am i suppose to do solving it by subtitution and how is it possible tof ind the constant term? or am i totally wrong?

**Physics Forums | Science Articles, Homework Help, Discussion**

Dismiss Notice

Join Physics Forums Today!

The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

# Homework Help: 1st order ODE Question

Can you offer guidance or do you also need help?

Draft saved
Draft deleted

**Physics Forums | Science Articles, Homework Help, Discussion**