# Thread: DiffEQ subspace of C^1

1. ## DiffEQ subspace of C^1

How would I solve this question?

d/dt y = λy λER (belongs to set of real numbers)
Show that the solutions of this ODE for a fixed λ - value form a 1-dimensional
subspace of C^1.

2. Originally Posted by thehollow89
How would I solve this question?

$\frac{dy}{dt} = \lambda y, \ \lambda \in \mathbb{R}$ (belongs to set of real numbers) Show that the solutions of this ODE for a fixed λ - value form a 1-dimensional subspace of C^1.
the set of solutions is the subspace generated by $y_1=e^{\lambda t}.$