Question

fill in the blank. Calc 2 Part a and b

Consider the following differential equation by" + 3y - 3y = 0 Exercise (a) satisfy the equation? For what values of r does the function y = e Step 1 in the To determine the values of r for which er satisfies the differential equation, we substitute f(x) = e equation, 67"(x) + 3f'(x) - 3f(x) = 0. Thus, we need to find f'(x) and "(x). f'(X) =

Answer 1

Solution Given differential Equation 69"+ By'- 3y=0 @ let the fonction +(x) = con We substitute f(x)= ex in the Equation 6f") + 3 f') – 3 474) 20 +(91)- egy $'() - root f'() = 7.7.2*4- 72"] : 6 g994 3.0.607 3ett 20 =) 3008 ( 2017 7-1) = 0 7 27478-170 of getta o 28+ 28-8-150 2017+1)-1(8+1)=0 (8+1 (28-D = 0 = r=-1 and r= 1/2 function y=aeoiden f(A)2 aeontol let

Cat us susatitute in 6f'(o) + 38'(*) – 3:4696 f(x)= a et be f'(a) = (acz)4 (134) = 0.7.276)EDE e to)= a 2 beden .: 6f"(*)+ 34') – 3+7) 20 16(qeybė") +3(_*)3(acu se?) -o - a to bet +2 a 2 ² 3607 3a 6² 35e? to a ae ( 4 + 2 2 - 2 ) + be (6-3-3) =0 -) aet6+6+12) + sé(0) = 6 =) 0 to 20 which is satisfying