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(Solved): Cooper Section 13.7 #1 a. What is the general solution of the equation y' = 3(1 - y)? (Use A as the ...
Cooper Section 13.7 #1 a. What is the general solution of the equation y' = 3(1 - y)? (Use A as the arbitrary constant.) b. What is the long term behaviour of solutions to this equation? (Draw diagrams to assist.) Oy1 as t→∞ y0 as t→ ∞ Oy-1 as t → ∞ Online Math Lab resources for this problem: • Differential Equations • Slope Fields
a. What is the general solution of the equation y′=3(1−y) ? (Use A as the arbitrary constant.) y(t)= b. What is the long term behaviour of solutions to this equation? (Draw diagrams to assist.) y→1 as t→∞y→0 as t→∞y→−1 as t→∞ Online Math Lab resources for this problem: - Differential Equations - Slope Fields
a. To find the general solution of the given differential equation, we can separate the variables and integrate: Separating variables: Integrating both sides: Using the substitution method, let's substitute Simplifying the integrals: where C is the constant of integration. Substituting back u=1?y: Taking the exponential of both sides: Since the absolute value of a quantity can be positive or negative, we can rewrite this as two cases: