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- https://math.libretexts.org/Courses/Red_Rocks_Community_College/MAT_2561_Differential_Equations_with_Engineering_Applications/02%3A_First_Order_Equations/2.03%3A_Substitution_Methods_-_Transformation_of_Nonlinear_Equations_into_Separable_Equations/2.3.01%3A_Autonomous_Second_Order_EquationsThis section deals with methods for dealing with a type of second order equation that often arises in applications of Newton's second law of motion, by reformulating it as first order equation wit...This section deals with methods for dealing with a type of second order equation that often arises in applications of Newton's second law of motion, by reformulating it as first order equation with a different independent variable. Although the method doesn't usually lead to an explicit solution of the given equation, it does provide valuable insights into the behavior of the solutions.
- https://math.libretexts.org/Courses/Mission_College/Math_3B%3A_Calculus_II_(Reed)/06%3A_Introduction_to_Differential_Equations/6.03%3A_Separable_EquationsWe now examine a solution technique for finding exact solutions to a class of differential equations known as separable differential equations. These equations are common in a wide variety of discipli...We now examine a solution technique for finding exact solutions to a class of differential equations known as separable differential equations. These equations are common in a wide variety of disciplines, including physics, chemistry, and engineering. We illustrate a few applications at the end of the section.
- https://math.libretexts.org/Courses/Mission_College/MAT_3B_Calculus_II_(Kravets)/06%3A_Introduction_to_Differential_Equations/6.03%3A_Separable_EquationsWe now examine a solution technique for finding exact solutions to a class of differential equations known as separable differential equations. These equations are common in a wide variety of discipli...We now examine a solution technique for finding exact solutions to a class of differential equations known as separable differential equations. These equations are common in a wide variety of disciplines, including physics, chemistry, and engineering. We illustrate a few applications at the end of the section.
- https://math.libretexts.org/Courses/City_College_of_San_Francisco/CCSF_Calculus_II__Integral_Calculus_._Lockman_Spring_2024/07%3A_Introduction_to_Differential_Equations/7.03%3A_Separable_EquationsWe now examine a solution technique for finding exact solutions to a class of differential equations known as separable differential equations. These equations are common in a wide variety of discipli...We now examine a solution technique for finding exact solutions to a class of differential equations known as separable differential equations. These equations are common in a wide variety of disciplines, including physics, chemistry, and engineering. We illustrate a few applications at the end of the section.
- https://math.libretexts.org/Courses/Chabot_College/Math_4%3A_Differential_Equations_(Dinh)/03%3A_Applications_of_First_Order_Equations/3.04%3A_Autonomous_Second_Order_EquationsThis section deals with methods for dealing with a type of second order equation that often arises in applications of Newton's second law of motion, by reformulating it as first order equation wit...This section deals with methods for dealing with a type of second order equation that often arises in applications of Newton's second law of motion, by reformulating it as first order equation with a different independent variable. Although the method doesn't usually lead to an explicit solution of the given equation, it does provide valuable insights into the behavior of the solutions.
- https://math.libretexts.org/Bookshelves/Differential_Equations/Ordinary_Differential_Equations_(Wiggins)/01%3A_Getting_Started_-_The_Language_of_ODEsThis is a course about ordinary differential equations (ODEs). So we begin by defining what we mean by this term.
- https://math.libretexts.org/Courses/Lake_Tahoe_Community_College/Interactive_Calculus_Q2/04%3A_Introduction_to_Differential_Equations/4.04%3A_Separable_EquationsWe now examine a solution technique for finding exact solutions to a class of differential equations known as separable differential equations. These equations are common in a wide variety of discipli...We now examine a solution technique for finding exact solutions to a class of differential equations known as separable differential equations. These equations are common in a wide variety of disciplines, including physics, chemistry, and engineering. We illustrate a few applications at the end of the section.
- https://math.libretexts.org/Bookshelves/Calculus/Book%3A_Active_Calculus_(Boelkins_et_al.)/07%3A_Differential_Equations/7.02%3A_Qualitative_Behavior_of_Solutions_to_Differential_EquationsSince the derivative at a point tells us the slope of the tangent line at this point, a differential equation gives us crucial information about the tangent lines to the graph of a solution. We will u...Since the derivative at a point tells us the slope of the tangent line at this point, a differential equation gives us crucial information about the tangent lines to the graph of a solution. We will use this information about the tangent lines to create a slope field for the differential equation, which enables us to sketch solutions to initial value problems. Our aim will be to understand the solutions qualitatively.
- https://math.libretexts.org/Courses/Cosumnes_River_College/Math_401%3A_Calculus_II_-_Integral_Calculus/06%3A_Introduction_to_Differential_Equations/6.03%3A_Separable_EquationsWe now examine a solution technique for finding exact solutions to a class of differential equations known as separable differential equations. These equations are common in a wide variety of discipli...We now examine a solution technique for finding exact solutions to a class of differential equations known as separable differential equations. These equations are common in a wide variety of disciplines, including physics, chemistry, and engineering. We illustrate a few applications at the end of the section.
- https://math.libretexts.org/Bookshelves/Calculus/Calculus_(OpenStax)/08%3A_Introduction_to_Differential_Equations/8.03%3A_Separable_EquationsWe now examine a solution technique for finding exact solutions to a class of differential equations known as separable differential equations. These equations are common in a wide variety of discipli...We now examine a solution technique for finding exact solutions to a class of differential equations known as separable differential equations. These equations are common in a wide variety of disciplines, including physics, chemistry, and engineering. We illustrate a few applications at the end of the section.
- https://math.libretexts.org/Courses/Monroe_Community_College/MTH_225_Differential_Equations/04%3A_Applications_of_First_Order_Equations/4.04%3A_Autonomous_Second_Order_EquationsThis section deals with methods for dealing with a type of second order equation that often arises in applications of Newton's second law of motion, by reformulating it as first order equation wit...This section deals with methods for dealing with a type of second order equation that often arises in applications of Newton's second law of motion, by reformulating it as first order equation with a different independent variable. Although the method doesn't usually lead to an explicit solution of the given equation, it does provide valuable insights into the behavior of the solutions.