Mister exam

Differential equations step by step

Differential equation
with unknown function ()

For Cauchy problem:

y() =
y'() =
y''() =
y'''() =
y''''() =

The graph:

from to

    Examples of differential equations

    What can the calculator of differential equations do?

    • Detailed solution for:
      • Ordinary Differential Equation (ODE)
      • Separable Differential Equation
      • Bernoulli equation
      • Exact Differential Equation
      • Second Order Differential Equation
      • Second Order Differential Equation
      • Homogeneous Differential Equation
      • Non Homogeneous Differential Equation
      • Substitution Differential Equation
      • A system of ordinary differential equations (System of ODEs)
    • Plot of graphs of solution set
    • The solution of the Cauchy problem
    • Classification of differential equations
    • Examples of numerical solutions

    The above examples also contain:

    • the modulus or absolute value: absolute(x) or |x|
    • square roots sqrt(x),
      cubic roots cbrt(x)
    • trigonometric functions:
      sinus sin(x), cosine cos(x), tangent tan(x), cotangent ctan(x)
    • exponential functions and exponents exp(x)
    • inverse trigonometric functions:
      arcsine asin(x), arccosine acos(x), arctangent atan(x), arccotangent acot(x)
    • natural logarithms ln(x),
      decimal logarithms log(x)
    • hyperbolic functions:
      hyperbolic sine sh(x), hyperbolic cosine ch(x), hyperbolic tangent and cotangent tanh(x), ctanh(x)
    • inverse hyperbolic functions:
      hyperbolic arcsine asinh(x), hyperbolic arccosinus acosh(x), hyperbolic arctangent atanh(x), hyperbolic arccotangent acoth(x)
    • other trigonometry and hyperbolic functions:
      secant sec(x), cosecant csc(x), arcsecant asec(x), arccosecant acsc(x), hyperbolic secant sech(x), hyperbolic cosecant csch(x), hyperbolic arcsecant asech(x), hyperbolic arccosecant acsch(x)
    • rounding functions:
      round down floor(x), round up ceiling(x)
    • the sign of a number:
      sign(x)
    • for probability theory:
      the error function erf(x) (integral of probability), Laplace function laplace(x)
    • Factorial of x:
      x! or factorial(x)
    • Gamma function gamma(x)
    • Lambert's function LambertW(x)

    The insertion rules

    The following operations can be performed

    2*x
    - multiplication
    3/x
    - division
    x^2
    - squaring
    x^3
    - cubing
    x^5
    - raising to the power
    x + 7
    - addition
    x - 6
    - subtraction
    Real numbers
    insert as 7.5, no 7,5

    Constants

    pi
    - number Pi
    e
    - the base of natural logarithm
    i
    - complex number
    oo
    - symbol of infinity
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