Can anyone show me the starting step for this question?

Question

Let $x = x(t)$ and $y = y(t)$ be functions in $t$. Suppose that $x′ = 2x − 5y + t$ and $y′ = 4x + 9y + \sin t$ such that $x(0) = y(0) = 0$. Find $y(1)$

This is my first time using maple.I know how to solve for a differential equation but this one got 3 variables. How to solve it?

Answer 1

You can simply see this as a system of differential equations that reads \begin{align*} x'(t) & = 2x-5y+t \\ y'(t) & = 4x+9y+\sin(t) \end{align*} Now you can solve this for $\begin{pmatrix} x(t)\\ y(t)\end{pmatrix}$ by using dsolve().

This actually gives you a bit more information than you need: You just want to calculate $y(1)$, but maple actually gives you $x(t)$, too.

Answer 2

Sol:= dsolve({
     diff(x(t), t) = 2*x(t) - 5*y(t) + t, 
     diff(y(t), t) = 4*x(t) + 9*y(t) + sin(t),
     x(0)=0, y(0)=0
});
eval(Sol, t= 1);