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- https://math.libretexts.org/Courses/Coastline_College/Math_C285%3A_Linear_Algebra_and_Diffrential_Equations_(Tran)/12%3A_First_order_ODEs/12.02%3A_Slope_fieldsThe general first order equation we are studying looks like y′=f(x,y). In general, we cannot simply solve these kinds of equations explicitly. It would be nice if we could at least figure out the sha...The general first order equation we are studying looks like y′=f(x,y). In general, we cannot simply solve these kinds of equations explicitly. It would be nice if we could at least figure out the shape and behavior of the solutions, or if we could find approximate solutions.
- https://math.libretexts.org/Courses/Lake_Tahoe_Community_College/MAT-204%3A_Differential_Equations_for_Science_(Lebl_and_Trench)/02%3A_First_order_ODEs/2.02%3A_Slope_fieldsThe general first order equation we are studying looks like y′=f(x,y). In general, we cannot simply solve these kinds of equations explicitly. It would be nice if we could at least figure out the sha...The general first order equation we are studying looks like y′=f(x,y). In general, we cannot simply solve these kinds of equations explicitly. It would be nice if we could at least figure out the shape and behavior of the solutions, or if we could find approximate solutions.
- https://math.libretexts.org/Bookshelves/Differential_Equations/Differential_Equations_for_Engineers_(Lebl)/1%3A_First_order_ODEs/1.2%3A_Slope_fieldsThe general first order equation we are studying looks like y???=f(x,y). In general, we cannot simply solve these kinds of equations explicitly. It would be nice if we could at least figure out the s...The general first order equation we are studying looks like y???=f(x,y). In general, we cannot simply solve these kinds of equations explicitly. It would be nice if we could at least figure out the shape and behavior of the solutions, or if we could find approximate solutions.
- https://math.libretexts.org/Courses/Mt._San_Jacinto_College/Differential_Equations_(No_Linear_Algebra_Required)/02%3A_First_Order_Equations/2.02%3A_Slope_FieldsA solution, that is, the graph of the solution, would be a curve that follows the slopes we drew. By looking at the slope field we get a lot of information about the behavior of solutions without havi...A solution, that is, the graph of the solution, would be a curve that follows the slopes we drew. By looking at the slope field we get a lot of information about the behavior of solutions without having to solve the equation. We can use a computer software to obtain a slope field of a differential equation, such as the GeoGebra slope field generator below. The video below shows how to use the GeoGebra slope field genereator to reproduce a slope field of a differential equation.
