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Magazine Problem 4
Verifying a Solution In Exercises \(1-8,\) verify the solution of the differential equation. $$ y^{2}-2 \ln y=x^{2} \quad \frac{d y}{d x}=\frac{x y}{y^{2}-1} $$
Problem 4
Finding a General Solution Using Separation of Variables In Exercises \(1-14,\) find the general solution of the differential equation. $$ \frac{d y}{d x}=\frac{6-x^{2}}{2 y^{3}} $$
Problem 4
Determining Whether a Differential Equation Is Linear In Exercises \(1-4,\) determine whether the differential equation is linear. Explain your reasoning. $$ \frac{2-y^{\prime}}{y}=5 x $$
Problem 4
Solving a Differential Equation In Exercises \(1-10\) , solve the differential equation. $$ \frac{d y}{d x}=6-y $$
Problem 5
Solving a Differential Equation In Exercises \(1-10\) , solve the differential equation. $$ y^{\prime}=\frac{5 x}{y} $$
Problem 5
Finding a General Solution Using Separation of Variables In Exercises \(1-14,\) find the general solution of the differential equation. $$ \frac{d r}{d s}=0.75 r $$
Problem 5
Verifying a Solution In Exercises \(1-8,\) verify the solution of the differential equation. $$ y=C_{1} \sin x-C_{2} \cos x \quad y^{\prime \prime}+y=0 $$
Problem 5
Solving a First-Order Linear Differential Equation In Exercises \(5-14,\) solve the first-order linear differential equation. $$ \frac{d y}{d x}+\left(\frac{1}{x}\right) y=6 x+2 $$
Problem 6
Finding a General Solution Using Separation of Variables In Exercises \(1-14,\) find the general solution of the differential equation. $$ \frac{d r}{d s}=0.75 s $$
Problem 6
Solving a Differential Equation In Exercises \(1-10\) , solve the differential equation. $$ y^{\prime}=-\frac{\sqrt{x}}{4 y} $$
