Find y as a function of x if y6y8y9ex with initial values y0

Find y as a function of x if: y\'\'\'-6y\'\'+8y\'=9e^x, with initial values y(0)=19, y\'(0)=20, y\'\'(0)=23

Solution

y\'\'\'-6y\'\'+8y\'=9e^x

sol: derivative of Y\'\'\'=3y^2

derivative of Y\'\'=2Y

derivative of Y\'=1

derivative of e^x=e^x

d/dx (Y\'\'\'-6Y\'\'+8y\'=9e^x)

3y\'\'-6x2y\'+8y=9e^x

3(23)-12(20)+8(19) = 9e^x

69-240+152=9e^x

-19=9e^x

e^x=(-19/9)

x=log ((-19)/9)

x=0.324511092 + 1.36437635 i