Solve the initial value problem y' = t * t, y(0) = 1, where * is the convolution operator.

For the Cauchy-Euler equation x2y''+xy'+y=x2 if you substitute z=ln(x), y'=(1/x)(dy/dz), and y''=(-1/x2)(dy/dz)+(1/x2)(d2y/dz2) into the original equation, it will transform to the equation a(d2y/dz2)+b(dy/dz)+cy=e2z Then a+b+c=? Fill in the equation mark using one of the following answer choices. (a) 0 (b) 1 (c) 2 (d) 3 (e) 4

Let h(t) Then h' (t) is h' (3) is = 2+³.2 h'' (t) is and h'' (3) is 6t 3.2 I

Find Yn(t) of the zero-input response if y(0)=1 and y’(0)= -2 for (D^2 +4D+8)y(t)= (D)x(t)