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(1 point) A first order linear equation in the form y' + p(x)y = f(x) can...

(1 point) A first order linear equation in the form y + p(x)y = f(x) can be solved by finding an integrating factor u(x) = e

(1 point) A first order linear equation in the form y' + p(x)y = f(x) can be solved by finding an integrating factor u(x) = expl (1) Given the equation xy' + (1 +4x) y = 10xe 4* find y(x) = (2) Then find an explicit general solution with arbitrary constant C. y = (3) Then solve the initial value problem with y(1) = e-4 y =
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Answer #1

(W xy+(1+4x)4 = 10 xě 4 ~ y +(1+43) y = loxes = y + ( + 4) 9 = 10ete Compare y+ P(x). Y = Q(x) P(x) = +4, Q(x) = loē u dii) (1) - ēt provide Froma, 9(1) = 56.249%+0.60724 (1) - 4 = sē4 +cieu =) A = (ste) > 5+C =) =) C= 1-5= -4 Again, . from u y

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