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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 › Initial value problems

    Solving initial value problems

    In this section, you will learn how to find the general solution to a differential equation, and use the general solution to solve an initial value problem.

    \(\dfrac{dy}{dx} = 2x + 1{\quad}y(0) = 3\)
    \(y = x^2 + x + 3\)
    137829Initial Value Problem (KristaKingMath)
    Krista King
    \(\dfrac{dy}{dx} = 6x - 3{\quad}y(0) = 4\)
    \(y = 3x^2 - 3x + 4\)
    137826Initial Value Problem
    The Organic Chemistry Tutor
    \(\dfrac{dy}{dx} = 2xy{\quad}y(0) = 3\)
    \(y = 3e^{x^2}\)
    137826Initial Value Problem
    The Organic Chemistry Tutor