OpenStudy (mony01):

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

3 years ago
OpenStudy (anonymous):

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...

3 years ago
OpenStudy (anonymous):

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

3 years ago
OpenStudy (anonymous):

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

3 years ago
OpenStudy (anonymous):

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

3 years ago
OpenStudy (anonymous):

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

3 years ago