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2 years ago

Solve the given differential equation by undetermined coefficients. y'' 4y = 7 sin(2x)

Mathematics

1 answer:

kherson [118]2 years ago

8 0

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

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3 years ago

How do i solve this proportion? 3t/10 = 1/2

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Step-by-step explanation:

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3 years ago

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lisov135 [29]

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Step-by-step explanation:

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3 years ago

Given f(x)=-2x-1, solve for x when f(x)=-7

Svetlanka [38]

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Step-by-step explanation:

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2 years ago

A meter stick casts a shadow 2.4 m long at the same time a flagpole casts a shadow 9.7 m long. How tall is the flagpole

Luda [366]

The first thing we are going to do is draw a diagram of the situation to help us to solve the situation.
We an draw tow similar triangle between the length of the shadows and the height of the stick and the pole.
Since <span>meter stick has a length of 1 meter, the height of our smaller triangle is 1 meter. Let </span> $h$ be height of of the pole. Since both triangles are similiar we can establish a proportion between their corresponding sides and solve for $h$ :
$\frac{h}{1} = \frac{9.7}{2.4}$
$h=\frac{9.7}{2.4}$
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We can conclude that the pole is 4.04 meters tall.

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3 years ago