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// about the analytical integration for the analytical solution
//Eg-13.4
//pg-529
clear
clc
x(1) = 0;
yb(1) = 0;
y(1) = 1; //Initial condition
h = 0.1;
deff('out = func(in1,in2)','out = 0.5*(1+in1)*in2^2')
//Taking the exact values using the expression calculated analytically as y = 4/(4-2*x-x^2)
z(1) = exp(x(1)^3/3);
for(i = 2:11)
x(i) = 0.1+(i-2)*0.1;
z(i+1) = 4/(4-2*x(i)-x(i)^2);
end
for(i = 1:10)
yb(i+1) = y(i) + h*func(x(i),y(i));
y(i+1) = y(i) + h/2*(func(x(i),y(i)) + func(x(i+1),yb(i+1)));
end
printf(' x yPc yExact\n')
for(i = 2:11)
printf('%f %f %f\n',x(i),y(i),z(i+1))
end
printf('\nSolving analytically gives :\n')
printf('y = 4/(4-2*x-x^2)\n')
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