General solution of differential equation calculator with steps

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Examples of differential equations

• The simplest differential equations of 1-order

• y' + y = 0

• y' - 5*y = 0

• x*y' - 3 = 0

• Differential equations with separable variables

• (x-1)*y' + 2*x*y = 0

• tan(y)*y' = sin(x)

• Linear inhomogeneous differential equations of the 1st order

• y' + 7*y = sin(x)

• Linear homogeneous differential equations of 2nd order

• 3*y'' - 2*y' + 11y = 0

• Exact Differential Equations

• dx*(x^2 - y^2) - 2*dy*x*y = 0

• Solve a differential equation with substitution

• x^2*y' - y^2 = x^2

• Change y(x) to x in the equation

• x^2*y' - y^2 = x^2

• Other

• -6*y - 5*y'' + y' + y''' + y'''' = x*cos(x) + sin(x)

What can the calculator of differential equations do?

• Detailed solution for:
  • Ordinary Differential Equation (ODE)
  • Separable Differential Equation
  • Bernoulli equation
  • Exact Differential Equation
  • First-order differential equation
  • Second Order Differential Equation
  • Third-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)
• Trigonometric integrals: Si(x), Ci(x), Shi(x), Chi(x)

The insertion rules

The following operations can be performed

Constants

How do you find the general solution of a differential equation?

How do you solve a differential equation step by step?

What is the general formula of differential equation?

What is general solution of PDE?