For each of the following operators and transforms, check if it's linear: 1. derivative, i.e., L[y]...

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For each of the following operators and transforms, check if it's linear: 1. derivative, i.e., L[y] =y', 2. second derivative, i.e., L[y] =y", 3. integral, i.e., L[y] = f y(t) dt, 4. Laplace transform, i.e., L[y] = {y}, where L{y}(s) = f y(t)e-st dt, 5. L[y] = yy'. For each of the following operators and transforms, check if it's linear: 1. derivative, i.e., L[y] =y', 2. second derivative, i.e., L[y] =y", 3. integral, i.e., L[y] = f y(t) dt, 4. Laplace transform, i.e., L[y] = {y}, where L{y}(s) = f y(t)e-st dt, 5. L[y] = yy'.