Question

For the IVP y' = t/y, y(0) = 1, Find Euler approximate solution values at t=0.1, t=0.2, t=0.3, with h=0.1

Answer 1

The Euler method for differential equation is a first order Runge-Kutta method family in which:
y_(i+1) = y_(i) + k1*h, where k1 = y'(t_(i), y_(i))
so...

Answer 2

we have that y_(0) = 1 and h=0.1

Answer 3

for i=0:
y_(1) = y_(0) + y'(t_(0), y_(0))*h
y_(1) = 1 + (0/1)*0.1
y_(1) = 1 => y(0.1) = 1

Answer 4

for i=1:
y_(2) = y_(1) + y'(t_(1), y_(1))*h
y_(2) = 1 + (0.1/1)*0.1
y_(2) = 1.01 => y(0.2) = 1.01

Answer 5

for i=2:
y_(3) = y_(2) + y'(t_(2), y_(2))*h
y_(3) = 1.01 + (0.2/1.01)*0.1
y_(3) = 1.029801980 => y(0.3) = 1.029801980