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    • ▾Differential equations
      • •Logistic growth
      • ▾Basic concepts of differential equations
        • •Intro to differential equations
        • •Verifying solutions to differential equations
        • •Sketching slope fields
        • •Sketching solution curves in slope fields
      • •Matching slope fields with equations
      • ▸Initial value problems
        • •Intro to initial value problems
        • •Solving initial value problems
      • ▸First order differential equations
        • •Separable first order differential equations
        • •Bernoulli differential equations
        • ▸Equilibrium solutions
          • •Intro to equilibrium solutions
        • •Euler's method
        • •Exact first order differential equations
        • •First order homogeneous differential equations
        • •Intervals of validity
        • •Solving first-order linear differential equations
      • ▸Second order differential equations
        • •Undetermined coefficients
        • •Reduction of order
        • •Variation of parameters
      • •Laplace transforms
      • ▸Systems of differential equations
        • •Solving systems of differential equations
        • •Real eigenvalues
      • •Partial differential equations
     › Differential equations › Basic concepts of differential equations

    Sketching solution curves in slope fields

    In this section, you will learn how to find a linear approximation to a separable differential equation by sketching a solution curve passing through a given point on a given slope field.

    Typeset a grid of points with axes where the axes are dashed lines. We don't want solid axes, because the slope at those points may be zero, in which case the student should draw a short horizontal line. Using dashed axes ensures the short lines are visible.

    YouTube videos

    • 137832Sketching direction fields (KristaKingMath)
      Krista King
    • 137833Slope Fields Linear Approximation Separable Differential Equation Calculus FRQ
      ProfRobBob
    • 137834How to sketch the particular equation from the slope field
      Brian McLogan