2nd order ODE

Mar 2016
5
0
USA
Given y''(t)+7x'(t)= 0 with x'(0)=a constant U

Solve for y'

Can l integrate the above ODE directly with respect to a variable t? hence,

y'(t)=-7x(t)

Thanks
 

romsek

MHF Helper
Nov 2013
6,738
3,034
California
Given y''(t)+7x'(t)= 0 with x'(0)=a constant U

Solve for y'

Can l integrate the above ODE directly with respect to a variable t? hence,

y'(t)=-7x(t)

Thanks
yes but there will be a constant of integration

$y^\prime(t) = -7x(t) + C$
 
Mar 2016
5
0
USA
And if y'(t) = a constant V, then C=v+7x(t) ?
 

HallsofIvy

MHF Helper
Apr 2005
20,249
7,909
And if y'(t) = a constant V, then C=v+7x(t) ?
Yes, but how do you know that y' is a constant? Do you mean y'(0)= V? (If so there is no need to say "a constant".)