The solution to the given differential equation is yp=−14xcos(2x)
The characteristic equation for this differential equation is:
P(s)=s2+4
The roots of the characteristic equation are:
s=±2i
Therefore, the homogeneous solution is:
yh=c1sin(2x)+c2cos(2x)
Notice that the forcing function has the same angular frequency as the homogeneous solution. In this case, we have resonance. The particular solution will have the form:
yp=Axsin(2x)+Bxcos(2x)
If you take the second derivative of the equation above for yp , and then substitute that result, y′′p , along with equation for yp above, into the left-hand side of the original differential equation, and then simultaneously solve for the values of A and B that make the left-hand side of the differential equation equal to the forcing function on the right-hand side, sin(2x) , you will find:
A=0
B=−14
Therefore,
yp=−14xcos(2x)
For more information about differential equation, visit
brainly.com/question/18760518
The answer is C your welcome Gn
Answer:
A
Step-by-step explanation:
A is the only answer with ordered pairs that have a consistent rate of change, -1/3
Step-by-step explanation:
<h2>[1]</h2>
- SI = $250
- Rate (R) = 12
% - Time (t) = 4 years
Therefore principal is $500.
<h2>__________________</h2>
<h2>[2]</h2>
- 2/7 of the balls are red.
- 3/5 of the balls are blue.
- Rest are yellow.
- Number of yellow balls = 36
Let the total number of balls be x.
→ Red balls + Blue balls + Yellow balls = Total number of balls
Total number of balls is 315.
A/Q,
3/5 of the balls are blue.
