Solve the given integral equation for LaTeX: y(t)y ( t ). LaTeX: y(t)+9\displaystyle{\int_{0}^{t}e^{ 9(t-v)}y(v)\, dv}=\sin(3t)y ( t ) + 9 ∫ 0 t e 9 ( t − v ) y ( v ) d v = sin ⁡ ( 3 t ) Group of answer choices LaTeX: y(t)=3\cos(3t)+9\sin(3t)-9 y ( t ) = 3 cos ⁡ ( 3 t ) + 9 sin ⁡ ( 3 t ) − 9 LaTeX: y(t)=3\cos(3t)+\sin(3t)-3 y ( t ) = 3 cos ⁡ ( 3 t ) + sin ⁡ ( 3 t ) − 3 LaTeX: y(t)=3\cos(3t)+\sin(3t) y ( t ) = 3 cos ⁡ ( 3 t ) + sin ⁡ ( 3 t ) LaTeX: y(t)=3\cos(3t)+9\sin(3t) y ( t ) = 3 cos ⁡ ( 3 t ) + 9 sin ⁡ ( 3 t ) LaTeX: y(t)=\cos(3t)+3\sin(3t)-3

Looks like the equation is

Differentiating both sides yields the linear ODE,

or

Multiply both sides by the integrating factor :

Integrate both sides, then solve for :

The given answer choices all seem to be missing C, so I suspect you left out an initial condition. But we can find one; let , then the integral vanishes and we're left with . So

So the particular solution is

step-by-step explanation:

answer: the answer is one

step-by-step explanation:

pemdas, in this situation there is no parenthesis or exponents so you go to multiplication, 1x1=1, then division 1/1= 1 then addition 1+1=2 then subtraction 2-1=1