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- Solve each of the following systems of differential equations. dx1dt=2x1+7x2+t dx2dt=7x1+2x2+2tWhich of the following equations can be reduced to the homogenuous linear differential equation with constant coefficient? d³y O a. 3. dr3 d?y dy + 2x2. + 7x- dx? da O b. , dy 2. + 22. dr3 d²y dy 71- dx %3D dr? Oc. + 23 dy dx? dy + 7x4. da %3D da3 O d. 3 dy d?y dy + 2x- + 7x- dr3 dx? dr + 2x2 d?y 7x Oe. d3y dy dr3 dr? daEvaluate. The differential is exact. (1,4,3) | (2xy? – 2xz2) dx + 2x²y dy – 2x²z dz (0,0,0) O A. 14 O B. 25 O C. 0 O D. 7 Click to select your answer.
- Which of the following classification of the differential equation, O A. dependent variable = x, second order, third degree, not linear O B. dependent variable = y, second order, third degree, linear O.C. dependent variable = x, second order, first degree, linear O. D. dependent variable = y, second order, first degree, not linear O E. All of the Choices OF. None of the Choices dx² 3 + 5 (dx - y = 0, is TRUE? dyPlease answer. This is linear differential equations.Let A and k be positive constants. Which of the given functions is a solution to 4 = -k(y+ A)? OA. y = -A + Ce-kt OB. y = A + Ce-kt Oc.y = A-1 +CeAkt OD. y = -A + Cekt OE. y = A + Cekt OF. y = A-1 +Ce-Akt
- For the differential equation given below, variable. d²x d1² + kx = Acost is the independent variable and is the dependentI. Classify each differential equations in terms of order, degree, dependent variable,independent variable, ordinary or partial, and linear or non-linear. If non-linear, state theterm where it is non-linear.What is the differential of a=3b+4b2−5b3+6b4