Write the order of the differential equation of the family of the following curves : (1) y=Ae^x + B e^( - Maths - Differential Equations

Question

Write the order of the differential equation of the family of the
following curves : (1) y=Ae^x + B e^( x+c)

Shruti Tyagi · Accepted Answer

Dear Student,

y=Aex+Bex+c   --1differentiating w r
t xdydx=Aex+Becex⇒y'=Aex+Bex+c ⇒y'=y--2differentiating again w
r
t x we gety''=y' ⇒y''=y⇒y''-y=0Hence required equation is y''=Aex+Bex+c Therefore the order of this equation is 2 as we have y''=d2ydx2
Regards,

Write the order of the differential equation of the family of the following curves : (1).y=Ae^x + B e^( x+c)