Question

Problem #7: Solve the following boundary value problem. y" - 12y + 36y 0, y) = 9, y(1) = 10 Problem #7: Enter your answer as a symbolic function of x, as in these examples Do not include 'y = 'in your answer. Just Save Submit Problem #7 for Grading Attempt #1 Attempt #2 Attempt #3 Attempt #4 Attempt #5 Problem #7 Your Answer: Your Mark: Problem #8: Solve the following initial value problem. y'"' – 9y" + 24y' – 16y = 0, y(0) = 0, y'(0) = 0, y"(0) = 4 Problem #8: Enter your answer as a symbolic function of x, as in these examples Do not include 'y = 'in your answer. Just Save Submit Problem #8 for Grading Attempt #1 Attempt #2 Attempt #3 Attempt #4 Attempt #5 Problem #8 Your Answer: Your Mark: Problem #9: Solve the following initial value problem. y" - 5y' + 4y = 5x + 4x, y0) = 0, y'(0) = 3 Problem #9: Enter your answer as a symbolic function of X, as in these examples Do not include 'y = 'in your answer. Just Save Submit Problem #9 for Grading

Answer 1

Given differential equation is y"-12y+36y = 0,y() = 9,y(1)= 10 d (D2-12D+36)y = 0 where D= Auxiliary equation or characteristic equation is p2 - 12r +36 = 0 The roote of the auxiliary equation p2 - 12r +36 = 0 =(r-6) = 0 r= 6,6 If the roots are real and equal then the complementary solution is y(x)=(4 +c2x)e® The general solution is y(x) = (C+c2x)e** y(0)=9 = y(0)= (+c(0)20) =9= (1) y(x) =(4 +02x) * y (1) =10 =10 = (6+) (2) 10 From (1), we get 10 = (9+c)20 =,= -9 6 The general solution is) sy(x)=(1+(209 -9)3]"