Verify that the vector X is a solution of the given homogeneous system. -1 x-(-; X'= 1 -1 x - (-²) 0² For X = 1 -5t/4 e , one has 1 16 X; X = -1. X'= 1 16 X= -1 -5t/4 A 100
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- Determine the particular solution of the ODE y”’ - 8y” + y’ + 42y = 2e^3x + 1 a. (-xe^3x / 10 - 1/42) b. (-xe^3x / 10 + 1/8) c. (-xe^3x / 5 + 1/8) d. (-xe^3x / 5 - 1/42)Find two linearly independent solutions of 2x^2)y'-ху'+(-1x+1)у-0,х>0 of the form y1=xr1(1+a1x+a2x2+a3x3+) y2=xr2(1+b1x+b2x2+b3x3+) where r1>r2. Enter r1= al= a2= a3= r2= b1= b2= b3Differentiate and simplify: y= (3 – 4x)2* O a.y'= - 2(3 – 4x)²x-4x + (3 – 4x)In(3 – 4x)] Ob.y'= 2(3 - 4x)2x-1[4x - (3 – 4x)In(3 – 4x)] O C. y'= - 2(3 - 4x)2x-1(4x - (3 – 4x)In(3 - 4x)] Od.y'= 2(3 - 4x)?* -!(4x + (3 – 4x)In(3 – 4x)]