# Error when trying to solve a linear differential equation

I am trying to solve a linear differential equation for the change in scale factor term, $$\delta a(t)$$, when mass terms are introduced to the equations of motion for General Relativity. The first equation I am have to solve is as follows:

$$\frac{d}{dt} \delta a(t) = \frac{8 \pi G (a(t))^2}{3 \frac{d}{dt}a(t)}[3m^2 (a(t))^2 \mp \frac{1}{2} \delta \rho (t)] + \frac{2\frac{d}{dt}a(t) \delta a(t)}{a}$$ This equation is of the form $$\frac{d}{dt} \delta a(t) + f(t) \delta a(t) = g(t)$$, which is a linear differential equation.

However, when I plug this equation into Mathematica, using the DSolve function, I receive an error to the degree of

Equation or list of equations expected instead of True in the first argument


My code is as follows:

DSolve[{\[Delta]a'[t] - (2*a'[t]*\[Delta]a[t])/a[t] == (
8*\[Pi]*G*(a^2)[t])/(
3*a'[t]) (3*m^2*(a^2)[t] - 1/2 \[Delta]\[Rho][t]), \[Delta]a ==
0, a == 1}, \[Delta]a[t], t]


where I have introduced the conditions that $$\delta a(0) = 0$$ and $$a(0) = 1$$.

What am I doing wrong here, is this just not numerically solvable?

Thanks!

Change (a^2)[t] to a[t]^2 and remove the condition a == 1 (NDSolve only accepts initial condition for \[Delta]a[t])
DSolve[{\[Delta]a'[t] - (2*a'[t]*\[Delta]a[t])/a[t] == (8*\[Pi]*G*a[t]^2)/(3*a'[t]) (3*m^2*a[t]^2 - 1/2 \[Delta]\[Rho][t]), \[Delta]a == 0 }, \[Delta]a[t], t]