If y(x) is a solution of y' = (y+1)(50 – y) with y(0) = 0, what is the limit of y(x) as x approaches +o ?

11.(Straightforward) Find a particular solution to each of these ODES by using the method of variation of parameters: (a) y" + y = sin(2x). (b) y" – y = x³. - (c) y" – 2y' + y = eK¤ . (Here K is an arbitrary constant..) - (d) y" – 2y' + y = x³ . -

Suppose f(): R² → R² and g(): R³ → R² are given by: ƒ = :)-(²) and ()-(7) = g 3y² + Find (f o g)'(x) at x = (₁) 2 y2 X3 = + X3

Suppose f(x) is differentiable at x = 2 and that f(2) = 3 and f′(2) = −4.