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Hello everyone.
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In this given question we have to find the solution for the initial value problem.
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The problem is 4 y -double -d -s minus 20 y -dash plus 25 y is equal to 0.
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The initial conditions which are given as y -gera as 2 and y -dash -0 is minus 3.
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So first we have to write the auxiliary equation for the differential equation.
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So 4 r squared minus 20 y 20 r, sorry, plus 25 is equal to 0.
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So we can write it as 2r minus 5 into 2 r minus 5 is equals to 0, right? so we get the roots as 5 by 2 and 5 by 2.
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Since both the roots are equal, so we have the general form for this equation.
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That is y is equals to c1, a to the power 2 .5x, plus c2x, a to the power 2 .5x.
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Right? and this is the general form of the given solution...