The characteristic equation for a 5th​ degree, homogeneous, constant coefficient DE is​ p(x)=x^3(x^2+1). Which linearly independent functions will be used to form the general​ solution?   A. ​1,x,x^2,cos(x),sin(x)   B. ​1,e^{-x},xe^{-x}, cos(x),sin(x)   C. ​x,x^2,x^3,cos(x),sin(x)   D. ​1,e^x,xe^x, cos(x),sin(x)

Q: Using [ y = e^(2x) (c1 + c2) + 3/2x2 (2x) ] and [ y = ( c1 + c2x ) e^(2x) + 3x/25 sinx + 4x/25 cnx +…

A: The given differential equation is;  y'' - 4y' + 4y = 3e2x + xsinx

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A: Given Functions are as follows

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Q: The solution of the following Bernoulli's equation y' + 3x²y = 4x²y² is: Oy= 3/(4+3Ce^(x^3 ) ) Oy=…

A: The given Bernoulli's equation is, y'+3x2y=4x2y2. To find: The solution of the given differential…

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A: Solve by separable variable method

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Q: Consider the estimated quadratic model   y ^ = 23 + 1.6x − 0.02x2. Now, Predict y when x equals 10,…

A: The objective is to find Predict y when x equals 10, 20, and 30.

Q: Find the solution. (403+12D²+13D+10)y = 0. @ y=c,e+e>(c,cosx + c sinx) +c,sinx) -3x y =…

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Q: ) = 3x + sin x - e^x solve using bisection method of non linear equations of one variable

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Q: Find the derivative of y = x°e*. O a. y' = 3e*x2(e*+x) O b. y 3x2(e* +1) O c. y = e*x2(x+ 3) O d. y'…

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A: Since you have asked multiple question, we will solve the first question for you. If you want any…

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Q: Solve the equation [cos (2y) - (3x^2)(y^2)]dx +[cos (2y) - 2x sin 2y - (2x^3)(y)]dy = 0

A: To solve the given differential equation. First we check whether the differential equation is exact…

Q: y'=sin (x) +8x3, y(0) = 2

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