Problem 3
Solving an Initial-Value Problem Using the method of separation of variables, solve the initial-value problem $$ y^{\prime}=(2 x+3)\left(y^{2}-4\right), \quad y(0)=-3 $$
Problem 3
What is the order of the following differential equation? $$ \left(x^{4}-3 x\right) y^{(5)}-\left(3 x^{2}+1\right) y^{\prime}+3 y=\sin x \cos x $$
Problem 3
For the following problems, consider the logistic equation in the form \(P^{\prime}=C P-P^{2} .\) Draw the directional field and find the stability of the equilibria.\(C=3\)
Problem 4
For the following problems, consider the logistic equation in the form \(P^{\prime}=C P-P^{2} .\) Draw the directional field and find the stability of the equilibria.\(C=0\)
Problem 4
Find the general solution to the differential equation \((x-2) y^{\prime}+y=3 x^{2}+2 x\). Assume \(x>2\)
Problem 4
Finding a Particular Solution Find the particular solution to the differential equation \(y^{\prime}=2 x\) passing through the point \((2,7)\).
Problem 4
Find the solution to the initial-value problem $$ 6 y^{\prime}=(2 x+1)\left(y^{2}-2 y-8\right), \quad y(0)=-3 $$ using the method of separation of variables.
Problem 5
Solve the initial-value problem $$ y^{\prime}+3 y=2 x-1, \quad y(0)=3 $$
Problem 5
Find the particular solution to the differential equation $$ y^{\prime}=4 x+3 $$ passing through the point \((1,7)\), given that \(y=2 x^{2}+3 x+C\) is a general solution to the differential equation.
Problem 5
For the following problems, consider the logistic equation in the form \(P^{\prime}=C P-P^{2} .\) Draw the directional field and find the stability of the equilibria.\(C=-3\)
