4 Find the general solution to y 2y 10y e ex Solutiongiven y

4. Find the general solution to y\" 2y\' 10y e ex

Solution

given y\'\'-2y\'+10Y=e^x

apply derivative on both sides

d/dx ( y\'\'-2y\'+10Y) = d/dx (e^x)

2y\'-2y+10 = e^x

again apply to derivative on both sides

2y-2=e^x

apply log on both sides

log (2y-2) = Log e^x

x=log 2y- log 2