If the initial value problem is 
and 
,y(0)=0 then y(t)=
.
Given the initial value problem be and ,y(0)=0.
We are required to find the solution of the given initial value problem.
Laplace transform is an integral transformation that converts a function of a real variable to a function of a complex variable.
Take laplace on the DE, we get
![s^{2}-sY(0)-y^{i}(0)-8[sY(s)-y(0)-15Y(s)]=0](https://tex.z-dn.net/?f=s%5E%7B2%7D-sY%280%29-y%5E%7Bi%7D%280%29-8%5BsY%28s%29-y%280%29-15Y%28s%29%5D%3D0)
(Putting the values given in question)
Y(s)=(
Y(s)=1/(
)
Simplifying the above:
=1/(
=1/[s(s-5)-3(s-5)]
=1/2 [1/(s-3)-1/(s-5)]
Taking inverse of the above we get,
y(t)=
Hence if the initial value problem is and ,y(0)=0 then y(t)=.
Learn more about laplace transform at brainly.com/question/17062586
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Answer:
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Step-by-step explanation:
Answer:
<em>Given-</em> y= -5x^2 +5
ATQ,
if it translated vertically downwards then the new function will be,
h = y - 5 = -5x^2
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Answer:
An event that is certain to happen has a probability of 1. An event that cannot possibly happen has a probability of zero. If there is a chance that an event will happen, then its probability is between zero and 1
Step-by-step explanation:
Answer:x+2y=6
Step-by-step explanation: Given points: (4,1) and (-4,5)
To find equation we need a slope and a point through which the line passes.
slope = (y1-y2)/(x1-x2)
= 1-5/4-(-4)
= -4/8
= -1/2
let the first point be the passing point,
eq. of a line: (y-y1)=slope(x-x1)
=(y-1)=-1/2(x-4)
=2y-2=-x+4
=x+2y=6
