Give the substitution that converts the given nonlinear equation into a linear equation then solve the initial value problem. y'-2y = y², y(0) = 1 a. y(x)=3/1+ v(x) = b. y(x) = — 2 1+e-2x c. y(x) = - d. y=3 e. y² = 1 e¹[t + 1 + e] t6 +1 2t3 5t 2+5 Ct5

Verify (do not solve) that y(x) = 3x + 2x-1/3 is a solution to 3xy' + y = 12x. %3D

Give the substitution that converts the given nonlinear equation into a linear equation then find the general solution y'-y=-y² a. y(x) = b. y(x)= d. y=3 e. y² = c. y(x) = - O a 1 1+ Ce=t e 2 1+e-2x 1 e'[t+1+e] t6 + 1 2t3 5t 2+5Ct5

Solve and identify the type of equilibrium point at the origin. x' 3 5.