Laplace transforms of a differential equation

Question

I have the following differentual equation $y'+4y=11t^7$ with the inital condition $y(0)=3$

I then have to calculate the Laplace transform of $y(t)$

I did the laplace tranform of $y(t)=11t^7$ which gave me the answer $\frac{55440}{s^8}$

I just want to make sure I have done this correctly or if I have selected the wrong value for $y(t)$

Answer 1

Applying Laplace transform we have $$ \mathcal{L}(y')+\mathcal{L}(4y)=\mathcal{L}(11t^7). $$ Then $$ s\mathcal{L}(y)-y(0)+4\mathcal{L}(y)=11\frac{7!}{s^{8}}. $$ Applying the initial condition we have $$ (s+4)\mathcal{L}(y)=11\frac{7!}{s^{8}}+3. $$