Question

Write a Maple program to solve analytically the ordinary differential equation dy dt = y 2 + 1 with initial condition y(0) = 0. What solution is found? Verify (on paper) that the solution found satisfies the differential equation and initial condition.

Answer 1

Here are the initializations that we need to make before we start solving ODEs in MAPLE

with (DEtools):

with (LinearAlgebra):

with (Plots):

First of all we need to enter the ode into MAPLE. Here is the code for entering the ODE

ode := diff(y(t),t) = y^2 + 1;

Now we enter what the unknown function is. In this case it is y(t).

fn := y(t);

Now, to input the initial condition

ic := y(0)=0;

To solve the ODE we use the dsolve function

sol := dsolve({ode,ic}, fn);

Then sol is the solution for the ODE. You can now print the value of sol and find the solution.