2. [5pts] Given that y 1, e are solutions to the homogeneous version of the nonhomogeneous...
5. Repeat the same questions in 4.) for the ODE Py"- tt+2)y+(t+2)y2t3, (t>0) (a) Find the general solution of the homogeneous ODE y"- 5y +6y 0. Particularly find yi and (b) Find the equivalent nonhomogeneous system of first order with the chan of variable y (c) Show that (nvand 2( re solutions of the homogeneous system of ODEs (d) Find the variation of parameters equations that have to be satisfic 1 for y(t) vi(t)u(t) + (e) Find the variation of...
(1 point In general for a non-homogeneous problem y' + p(x) +(z) = f() assume that y. is a fundamental set of solutions for the homogeneous problemy" p(x) + (2) 0. Then the formula for the particular solution using the method of variation of parameters is where (z)/ and ()/() where W() is the Wronskian given by the determinant W (2) (2) W2) 31(2)/(2) dr. NOTE When evaluating these indefinite integrals we take the W(2) So we have the de...
QUESTION 10 Note that yı(t) Vt and y(t) =t-1 are solutions of the linear homogeneous differential equation 2t²Y" + 3ty' – y=0. Use variation of parameters to find the general solution of the nonhomogeneous differential equation 2t’y" + 3ty' - y = 4t? + 4t. 8 2 OA Civt + Cat-1 + 74 35 oCivt+Cet-1 + 4 9 t2 + 2t OC Civt + Cat-1 + 4 9 t2 + 2 5 2 OD. 8 Civt + Cat-1 + t2...
Note that yı(t) = Vt and yz(t) = t-1 are solutions of the linear homogeneous differential equation 2t’y" + 3ty' – y = 0. Use variation of parameters to find the general solution of the nonhomogeneous differential equation 2t’y" + 3ty' - y = 4t² + 4t. 8 o* Civt + Cat-1 + + 35 OB. 4 Civt + Cat-1+ t + 2 t2 9 of Civt + Cat-1 + t2 + 2t 9 00 Civt + Cut-+ 4 OE...
Consider the nonhomogeneous second order linear equation of the form y" + 2y' + y = g(t). Given that the fundamental solution set of its homogeneous equation is {e**, te' } For each of the parts below, determine the form of particular solution y, that you would use to solve the given equation using the Method of Undetermined Coefficients. DO NOT ATTEMPT TO SOLVE THE COEFFICIENTS. a) y" + 2y' + y = 2te b) y" + 2y' + y...
In this problem you will use variation of parameters to solve the nonhomogeneous equation fy" + 4ty' + 2y = 1 + 12 A. Plug y = p into the associated homogeneous equation (with "0" instead of "13 + 12") to get an equation with only t and n. (Note: Do not cancel out the t, or webwork won't accept your answer!) B. Solve the equation above for n (uset # 0 to cancel out the t). You should get...
Find general solutions to the nonhomogeneous Cauchy–Euler equations using variation of parameters. t2y''+3ty'+y=t-1
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.
(1 point) The general solution of the homogeneous differential equation can be written as 2 where a, b are arbitrary constants and is a particular solution of the nonhomogeneous equation By superposition, the general solution of the equation 2y 5ryy 18z+1 isyp so yax-1+bx-5+1+3x NOTE: you must use a, b for the arbitrary constants. Find the solution satisfying the initial conditions y(1) 3, y'(1) 8 The fundamental theorem for linear IVPs shows that this solution is the unique solution to...
3. Given that yı(t) = t, y(t) = t, and yz(t) = are solutions to the homogeneous differential equation corresponding to ty" + t'y" – 2ty' + 2y = 2*, t > 0, use variation of parameters to find its general solution.