Question

Please explain step a. Thanks.

a. Setup the first order ODE necessary for variation of parameters. b. Determine the real valued general solution of the second order ODE in simplest form. u" – 3u' + 2u = (1 +e-x) -1 All the integration can be done. There's a helpful rewrite of the integrand that makes this easy.

Answer 1

e non homogenious Bit. gst necessary con let 1st order linear nonhomogeni 2.6) Y'+fⓇ9 = (a) — * necessary condition to solve by the variation of parameter coeficient of yl should be nonaeco in whole of Domain of a. .. 19.00) #01 Now by deviding do(?) the eq? Changed in the form 9+ $(T) 3 = k(x) - ) solution of homogenious Equation yl + f(a)9 50 = 100)= effcard or the solution to the non homogeneous equation y = U(T) V(X) = UCHD effcada go= urlt vul putt it in a UV'+ UV # fuv = kcal vultul vit fv) = K LO) —** .: @ V satisfied ** ut frao i Vu'ck(a)

g': Y (3) 14=5 K6823 SO, Ind necessary condition to solve by variation of parameter is that IV to then you uv 43(SKC39. da) yes + y 2 + c