91Ó°ÊÓ

Find the solution \(y(t)\) by recognizing each differential equation as determining unlimited, limited, or logistic growth, and then finding the constants. $$ \begin{array}{l} y^{\prime}=0 \\ y(0)=5 \end{array} $$

For each initial value problem, use an Euler's method graphing calculator program to find the approximate solution at the stated \(x\) -value, using 50 segments. [Hint: Use an interval that begins at the initial \(x\) -value and ends at the stated \(x\) -value. \(y^{\prime}=e^{x / y}\) \(y(1)=0.4\) Approximate the solution at \(x=3\)

Find the solution \(y(t)\) by recognizing each differential equation as determining unlimited, limited, or logistic growth, and then finding the constants. $$ \begin{array}{l} y^{\prime}=2(100-y) \\ y(0)=0 \end{array} $$

Solve each first-order linear differential equation. $$ y^{\prime}+(\cos x) y=\cos x $$

Find the general solution of each differential equation or state that the differential equation is not separable. If the exercise says "and check," verify that your answer is a solution. $$ y^{\prime}=\frac{x}{x^{2}+1} $$

Solve each first-order linear differential equation. $$ y^{\prime}-(\sin x) y=\sin x $$

For each initial value problem, use an Euler's method graphing calculator program to find the approximate solution at the stated \(x\) -value, using 50 segments. [Hint: Use an interval that begins at the initial \(x\) -value and ends at the stated \(x\) -value. \(y^{\prime}=1+\frac{y}{x}\) \(y(2)=-1\) Approximate the solution at \(x=3.5\)

Find the solution \(y(t)\) by recognizing each differential equation as determining unlimited, limited, or logistic growth, and then finding the constants. $$ \begin{array}{l} y^{\prime}=48(2-y) \\ y(0)=0 \end{array} $$

Find the general solution of each differential equation or state that the differential equation is not separable. If the exercise says "and check," verify that your answer is a solution. $$ y^{\prime}=x y^{2} $$

For each initial value problem, use an Euler's method graphing calculator program to find the approximate solution at the stated \(x\) -value, using 50 segments. [Hint: Use an interval that begins at the initial \(x\) -value and ends at the stated \(x\) -value. \(\frac{d y}{d x}=\sqrt{x+y}\) \(y(3)=1\) Approximate the solution at \(x=3.8\)