anyone here took a differential equations course?

[Omegachi]

i am totally stuck on this problem and don't know where to start:

verify that both phi(t)=1-t and psi(t)=-(t^2)/4 are solutions of the IVP

y'= (-t + sqrt(t^2+4y))/2 , y(2) = -1



if anyone knows what to do, please help me

 

[Ready]

Im pretty sure the answer is 5

 

[Suspicious-Teach8788]

Sorry buddy. There's a reason why I got a D+ in that course and I'm taking it again... Except we're only on linear algebra so far..

 

[Random Variable]

let y = 1 - t
then y' = -1

and (-t + sqrt(t^2 + 4 - 4t))/2 = (-t + sqrt((t - 2)^2))/2 = (-t + t - 2)/2 = -1

and obviously y(2)=-1

 

[BRObedoza]

just take the first derivative and substitute into the diff. eq.