If you have knowledge of differential equation please help me understand this one;

I was given this: d^2y/dx^2 + 2dy/dx = 5

and without showing how the complementary function that they got was: CF: y = Acos(sqrt(2)*x) +Bsin(sqrt(2)*x)

Please enlighten me if you know how this happened

Question

If you have knowledge of differential equation please help me understand this one;

I was given this: d^2y/dx^2 + 2dy/dx = 5

and without showing how the complementary function that they got was: CF: y = Acos(sqrt(2)*x) +Bsin(sqrt(2)*x)

Please enlighten me if you know how this happened

sirm3d · Answer

the complementary function is obtained from d^2y/dx^2 + 2y = 0,
NOT
d^2y/dx^2 +2dy/dx = 0

anonymous · Answer

can you please show me the steps taken..and take into consideration the "5" that's been equated by the eqn

sirm3d · Answer

assuming that the DE is $$\frac{ d^2y }{ dx^2 }+2\frac{ dy }{ dx }=5$$

sirm3d · Answer

the complementary function is $$y _{c}=c _{1}e^{-2x}+c_{2}$$

anonymous · Answer

that's what I got too, guess I'll have to check in with my teacher

anonymous · Answer

Thanks by the way