The general solution of the differential equation yn−9y=0 can be written in the form y(x)=Aem1x+Bem2x, where A,B,m1,m2∈R and m1&gt;m2. a) Solve the auxiliary equation, and enter the values of m1 and m2 in the boxes. Do not enter decimals in your answers. Enter whole numbers, fractions or square roots as appropriate. If you need to enter a square root, e.g. x, enter this as x. m1= ? m2= ?

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The general solution of the differential equation yn−9y=0 can be written in the form y(x)=Aem1x+Bem2x, where A,B,m1,m2∈R and m1&amp;gt;m2. a) Solve the auxiliary equation, and enter the values of m1 and m2 in the boxes. Do not enter decimals in your answers. Enter whole numbers, fractions or square roots as appropriate. If you need to enter a square root, e.g. x, enter this as x. m1= ? m2= ?

aprovard · Accepted Answer

Step 1: To Find We have to find the general solution of the differential equation y−9y=0 and write it in the form of y(x)=Aem1x+Bem2x. Step 2: Calculation y9y=0 Auxilary Equation: m2−9=0 m2−32=0 (m+3)(m−3)=0 m=−3,3 Since roots of the auxiliary equation are distinct and −3&amp;lt;3, then the solution is y(x)=Ae3x+Be−3x Hence m1=3 and m2=−3.

The general solution of the differential equationy^{n}-9y=0can b

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