Answer:
Step-by-step explanation:
Using linear differential equation method:
\frac{\mathrm{d} y}{\mathrm{d} x}+3y=e^5^x
I.F.= [tex]e^{\int {Q} \, dx }[/tex]
I.F.=[tex]e^{\int {3} \, dx }[/tex]
I.F.=[tex]e^{3x}[/tex]
y(x)=[tex]\frac{1}{e^{3x}}[\int {e^{5x}} \, dx+c][/tex]
y(x)=[tex]\frac{e^{2x}}{5}+e^{-3x}\times c[/tex]
substituting x=2
c=[tex]\frac{25-e^4}{5e^{-6}}[/tex]
Now
y=[tex]\frac{e^{2x}}{5}+e^{-3x}\times \frac{25-e^4}{5e^{-6}}[/tex]
