a.

dx/dz = 1 +x²+ z, x(1) = -4

Find the solution of the above ODE problem using the Integrating factor method.

b.

dx/dz = 2z + x, x(0)=5

For the solution above, make an approximation using Euler's formula with h=0.5 to get an approximation to y(1.5).

c.

Prove that the exact solution to the ODE in b. above utilizing the IF(Integrating Factor) method is given by x = 7e^z - 2z- 2