1st order diff (both), general term, euclidean and number bases

The particular solution of the differential equation

 $\frac{\text{d}y}{\text{d}x}+2y=x$ 

for which y=0 when x=0 is given by

 

•  $y=\frac{1}{2}x^2e^{-2x}$  

•  $y=\frac{e^{-2x}+2x-1}{4}$  

•  $y=1-e^{-2x}$  

•  $y=\frac{1-e^{-2x}}{2}$  

The general solution of the differential equation

 $\frac{\text{d}y}{\text{d}x}+y=2e^{-x}$ 

 is

•  $y=e^{-x}\left(A+2x\right)$  

•  $y=Ae^{-x}+2e^{-x}$  

•  $y=Ae^x+2xe^{-x}$  

•  $y=Ae^{-x}+Bxe^{-x}$  

The solution of linear differential equation  $\frac{\text{d}y}{\text{d}x}+y=e^x$  

•  $y=\frac{e^2+c}{4x^2}$  

•  $y=\frac{ex^2}{4}+c$  

•  $y=\frac{e^{4x}+c}{x^2}$  

•  $y=\frac{e^x}{2}+Ce^{-x}$  

Find the coefficient of x³ in the expansion of (1 + x)²⁰

• 1140

• 190

• 4845

• 8000

Find the coefficient of x⁴ in the expansion of (1 - x)¹⁴

• 1001

• -1001

• 364

• -364

Find the coefficient of x² in the expansion of (1 + 4x)⁹

• 576

• 36

• 144

• 1344

Find the GCF of 2415 and 3289 using Euclidean Algorithm: