Problem 71
Find the general solution to the differential equations. $$ y^{\prime}=y\left(x^{2}+1\right) $$
Problem 72
You throw two objects with differing masses \(m_{1}\) and \(m_{2}\) upward into the air with the same initial velocity \(a \mathrm{ft} / \mathrm{s}\). What is the difference in their velocity after 1 second?
Problem 72
Find the general solution to the differential equations. $$ y^{\prime}=e^{-y} \sin x $$
Problem 73
You throw two objects with differing masses \(m_{1}\) and \(m_{2}\) upward into the air with the same initial velocity \(a \mathrm{ft} / \mathrm{s}\). What is the difference in their velocity after 1 second?
Problem 73
Find the general solution to the differential equations. $$ y^{\prime}=3 x-2 y $$
Problem 74
Find the general solution to the differential equations. $$ y^{\prime}=y \ln y $$
Problem 74
[T] You throw a ball of mass 1 kilogram upward with a velocity of \(a=25 \mathrm{~m} / \mathrm{s}\) on Mars, where the force of gravity is \(g=-3.711 \mathrm{~m} / \mathrm{s}^{2}\). Use your calculator to approximate how much longer the ball is in the air on Mars.
Problem 75
Find the solution to the initial value problem. $$ y^{\prime}=8 x-\ln x-3 x^{4}, y(1)=5 $$
Problem 76
[T] A car on the freeway accelerates according to \(a=15 \cos (\pi t)\), where \(t\) is measured in hours. Set up and solve the differential equation to determine the velocity of the car if it has an initial speed of 51 mph. After 40 minutes of driving, what is the driver's velocity?
Problem 76
Find the solution to the initial value problem. $$ y^{\prime}=3 x-\cos x+2, y(0)=4 $$
