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8. Solve the following differential equations. You may leave your answers in implicit form unless it's easy to solve for the dependent variable. Show your work! dy (a) - y = e*y? dx dy (b) + y = xª ln x d.x dy (c) = e3x+2y dx

8. Solve the following differential equations. You may leave your answers in implicit form unless it's easy to solve for the dependent variable. Show your work! dy (a) - y = e*y? dx dy (b) + y = xª ln x d.x dy (c) = e3x+2y dx

Advanced Engineering Mathematics
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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Answer question 8 pls

### Problem 7 A skydiver weighs 125 pounds, and her parachute and equipment combined weigh another 35 pounds. After exiting from a plane at an altitude of 15,000 feet, she falls for 15 seconds. Assume that the constant of gravity has the value \( k = 0.5 \) during free fall and that \( g = 32 \), and assume that her initial velocity on leaving the plane is zero. (Hint: Use the solutions from the Linear Air Resistance model that were given on the last page of Section 3.1.) **(a)** Write the initial value problem that is associated with this scenario. **(b)** What is her velocity and how far has she traveled 15 seconds after leaving the plane? **(c)** What is her terminal velocity in free fall? --- ### Problem 8 Solve the following differential equations. You may leave your answers in implicit form unless it's easy to solve for the dependent variable. Show your work! **(a)** \(\frac{dy}{dx} = e^x y^2\) **(b)** \(\frac{dy}{dx} + y = x^4 \ln x\) **(c)** \(\frac{dy}{dx} = e^{3x+2y}\)
Transcribed Image Text:### Problem 7 A skydiver weighs 125 pounds, and her parachute and equipment combined weigh another 35 pounds. After exiting from a plane at an altitude of 15,000 feet, she falls for 15 seconds. Assume that the constant of gravity has the value \( k = 0.5 \) during free fall and that \( g = 32 \), and assume that her initial velocity on leaving the plane is zero. (Hint: Use the solutions from the Linear Air Resistance model that were given on the last page of Section 3.1.) **(a)** Write the initial value problem that is associated with this scenario. **(b)** What is her velocity and how far has she traveled 15 seconds after leaving the plane? **(c)** What is her terminal velocity in free fall? --- ### Problem 8 Solve the following differential equations. You may leave your answers in implicit form unless it's easy to solve for the dependent variable. Show your work! **(a)** \(\frac{dy}{dx} = e^x y^2\) **(b)** \(\frac{dy}{dx} + y = x^4 \ln x\) **(c)** \(\frac{dy}{dx} = e^{3x+2y}\)
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