Consider the following differential equations dydt ty y0 1

Consider the following differential equations dy/dt = ty, y(0) = 1 y\'/y - y = 0, y(1) = 2 Solve the differential equation, using Euler\'s method on [0, 1] for (I) and [1, 3] for (II). In both cases use two values of the stepsize h (h = 0.1 and h = 0.01)^1. Compute the error, using the exact solution

Solution

euler method = y_{n+1= yn+h f(xn,yn)}

_{1. dy/dt=ty y(0)=1}

_{x0=0 yo=1}

_h=0.1

_{y¹=1+(0.1)(0x1)}

_y(0,1)=1

_h=0.01

y¹=1+(0.01)(0X1)

y1 =1

2.y¹/y-y=0 y(1)=2

y1=y2

y1=1+0.1(3²)

=1.9

h=0.01

y₁=1+(0.01)(3²⁾

y₁ =1.09