11. please show all work and specify which letter answer
11. please show all work and specify which letter answer If one solution of the differential...
14. pleaae show all work and specify which letter answer 14 Giren two linearly independent solutions ye Y = xe of yl-2y ty=0, use the method of variation & Of parameters to find a particular solution of Y"-2y't y=e² -as yp= b) yp= dJ e) y.p = c) qp = X 4 2 xé X Yp=e z
10. pleaae show all work and specify which letter answer cs Vi=est Y2= xet 10 Two linearly independent solution of the differential equation Byl + Syl-zy o are a) y = e 6x b) yi-e6x Y2=ex d) vize ed y,=(2x 192 Y = e2x Ya=est
9. specify which letter answer a two lirearly independent solutions of the differential equation y"-1441-494-0 ore af y, =ė? .Yz-Xerx UX b) y, = e 1 Y2 = xex YZ = Xe²7 6 yi=ex d) es vize" Yo = ex Y2 = ex 77 1 Y = e-7x
Please show all work and steps! Would like to learn how! Given a second order linear homogeneous differential equation a2(x)y" + a1(x)y' + 20 (x)y = 0 we know that a fundamental set for this ODE consists of a pair linearly independent solutions Yı, Y2. But there are times when only one function, call it Yı, is available and we would like to find a second linearly independent solution. We can find Y2 using the method of reduction of order....
6. specify which letter answer Y2 = it has gereral solution? ssole differential equation y = et ? by separation of variables a) y = + Y + c 4X c) y=4e y 3+C 4 4x4 b) y = - - - © y = 46 (2x) +C e + C ddy- celky ux
Please help answer the 5 parts of this 1 question. Question 6 -2a is a solution to the following ODE:/" -2/-8y 0. Use Reduction of Order to find a y1 2nd linearly independent solution. [Select] Step 1: Let y- Select] [Se ue(-2x) Then y e-2x) Step 2: Substitu ue-8x) simplify to get [Select e-8x) Step 3: Reduce Step 4: Solve the equation for w. (Select] Step 5: Solve for u. Step 6. Identify the two linearly independent solutions e ae...
12. specify which letter answer is correct dj yp=é 2 Otwo linearly independene solotions of the I differential equation ý "+12ylt 36y=o are 064 Y₂ = Xe6x b) y,=0 Y = xe Y = 6x d Yizes Y = 0 6x Y = xe 6x Vi=e6x Y2= e 6x
Consider differential equation (x - 1)y" – xy' + y = 0. a). Show that yi = el is a solution of this equation. Use the method of reduction of order to find second linearly independent solution y2 of this equation. (2P.) b). Find solution of the initial value problem (1P.) y(1) = 0, y'(1) = 1. c). Find solution of the initial value problem (1P.) y(1) = 0, y'(1) = 0. d). Does your answer in b) and c)...
3. Consider the differential equation ty" - (t+1)y + y = t?e?', t>0. (a) Find a value ofr for which y = et is a solution to the corresponding homogeneous differential equation. (b) Use Reduction of Order to find a second, linearly independent, solution to the correspond- ing homogeneous differential equation. (c) Use Variation of Parameters to find a particular solution to the nonhomogeneous differ- ential equation and then give the general solution to the differential equation.
Given a second order linear homogeneous differential equation a2(x)” + a (x2y + a)(x2y = 0 we know that a fundamental set for this ODE consists of a pair linearly independent solutions yı, y. But there are times when only one function, call it yi, is available and we would like to find a second linearly independent solution. We can find y2 using the method of reduction of order. First, under the necessary assumption the az(x) + 0 we rewrite...