Is this the general solution for the DE y''+4y' +20y=0 with initial conditions?

  • Thread starter Thread starter RadiationX
  • Start date Start date
RadiationX
Messages
255
Reaction score
0
solve y''+4y' +20y=0 ;y(0)=-3 ,\\ y'(0)=5 is this the general solution?

e^{-2t}(C_1\cos{4t} + C_2\sin{4t})
 
Physics news on Phys.org
Yes. It is.
 
You don't need the general solution as the final answer,but the particular solution.

Daniel.
 
Thread 'Variable mass system : water sprayed into a moving container'

Thread 'Variable mass system : water sprayed into a moving container'

Starting with the mass considerations #m(t)# is mass of water #M_{c}# mass of container and #M(t)# mass of total system $$M(t) = M_{C} + m(t)$$ $$\Rightarrow \frac{dM(t)}{dt} = \frac{dm(t)}{dt}$$ $$P_i = Mv + u \, dm$$ $$P_f = (M + dm)(v + dv)$$ $$\Delta P = M \, dv + (v - u) \, dm$$ $$F = \frac{dP}{dt} = M \frac{dv}{dt} + (v - u) \frac{dm}{dt}$$ $$F = u \frac{dm}{dt} = \rho A u^2$$ from conservation of momentum , the cannon recoils with the same force which it applies. $$\quad \frac{dm}{dt}...
View full post »

Similar threads

Obtain a nonzero solution of ##y''-4y'+x^2(y'-4y)=0## by inspection
Replies
7
Views
2K
Understanding a math step in solving Schrödinger's equation for single particle in a box
Replies
8
Views
914
Position and acceleration in simple harmonic motion given velocity
Replies
16
Views
1K
MHB -1.8.17 initial value then find C
Replies
11
Views
1K
Estimating damped harmonic oscillator parameters from this plot of the oscillations
Replies
9
Views
2K
Finding velocity and position of ##a(t)=−\omega^2(C_1\cos\theta+C_2\sin\theta)##
Replies
12
Views
1K
How do we write a sinusoidal solution to a 2nd order DE as a sum of exponentials raised to complex roots?
Replies
2
Views
2K
I Solution of delayed forcing function
Replies
5
Views
3K
X and Y coordinates of an oscillating object on a spring.
Replies
3
Views
592
Finding the constants of the general approximate solution to a double pendulum
Replies
1
Views
862

Hot Threads

Recent Insights

Back
Top