Explanation Formula used: A first-order differential equation of the form d y d x = g ( x ) h ( y ) is said to be separable or to have separable variables. Calculation: Let u = y ′ , then the given equations become u ′ = 2 x u 2 Separate the variables d u u 2 = 2 x d x Integrate both sides − u − 1 = x 2 + c 2 Since u = y ′ , so − 1 y ′ = x 2 + c 1 − d x d y = x 2 + c 1 − 1 x 2 + c 1 d x = d y Integrate both sides y = − ∫ 1 x

Differential Equations with Boundary-Value Problems (MindTap Course List)

9th Edition

ISBN: 9781305965799

Author: Dennis G. Zill

Publisher: Cengage Learning

See similar textbooks

Concept explainers

Differential Equations

Have you ever observed the movement of the satellites and rockets or how the planets go around the sun in their orbits? How will you determine their motion? Definitely they follow some scientific laws and these kinds of problems are framed as differentia…

Videos

Question

Chapter 4.10, Problem 24E

To determine

Discuss how to find an alternative two-parameter family of solutions for the nonlinear differential equation y″=2x(y′)2. Carry out your ideas and solve the equation.

Expert Solution & Answer

Want to see the full answer?

Check out a sample textbook solution

See solution

Chapter 4.10, Problem 23E

Chapter 4.10, Problem 25E

Students have asked these similar questions

Show that the Laplace equation in Cartesian coordinates: J²u J²u + = 0 მx2 Jy2 can be reduced to the following form in cylindrical polar coordinates: 湯( ди 1 8²u + Or 7,2 მ)2 = 0.

Draw the following graph on the interval πT 5π < x < x≤ 2 2 y = 2 cos(3(x-77)) +3 6+ 5 4- 3 2 1 /2 -π/3 -π/6 Clear All Draw: /6 π/3 π/2 2/3 5/6 x 7/6 4/3 3/2 5/311/6 2 13/67/3 5 Question Help: Video Submit Question Jump to Answer

Determine the moment about the origin O of the force F4i-3j+5k that acts at a Point A. Assume that the position vector of A is (a) r =2i+3j-4k, (b) r=-8i+6j-10k, (c) r=8i-6j+5k

Chapter 4 Solutions

Differential Equations with Boundary-Value Problems (MindTap Course List)

Ch. 4.1 - In Problems 14 the given family of functions is...Ch. 4.1 - In Problems 14 the given family of functions is...Ch. 4.1 - In Problems 14 the given family of functions is...Ch. 4.1 - In Problems 14 the given family of functions is...Ch. 4.1 - Given that y=c1+c2x2 is a two-parameter family of...Ch. 4.1 - Find two members of the family of solutions in...Ch. 4.1 - Prob. 7E Ch. 4.1 - Use the general solution of x + 2x = 0 given in...Ch. 4.1 - In Problems 9 and 10 find an interval centered...Ch. 4.1 - In Problems 9 and 10 find an interval centered...

Knowledge Booster

Learn more about

Need a deep-dive on the concept behind this application? Look no further. Learn more about this topic, subject and related others by exploring similar questions and additional content below.

Discuss how to find an alternative two-parameter family of solutions for the nonlinear differential equation y ″ = 2 x ( y ′ ) 2 . Carry out your ideas and solve the equation.

Solution Summary: The author explains how to find an alternative two-parameter family of solutions for the nonlinear differential equation.

Concept explainers

Videos

Discuss how to find an alternative two-parameter family of solutions for the nonlinear differential equation y″=2x(y′)2. Carry out your ideas and solve the equation.

Want to see the full answer?

Chapter 4 Solutions