The teacher will be very surprised to see your correct solution ðŸ˜‰

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### 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
- hom*ogeneous Differential Equation
- Non hom*ogeneous 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

### 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 inhom*ogeneous differential equations of the 1st order
- y' + 7*y = sin(x)
- Linear hom*ogeneous 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
- Linear differential equations of the 3rd order
- y''' + 3*y'' + y' + 3y = 0
- y''' + 2*y'' + y' = exp(-x)
- y''' + 3*y'' + y' + 3y = sin(x) + 2
- Other
- -6*y - 5*y'' + y' + y''' + y'''' = x*cos(x) + sin(x)

Learn more about Differential equations

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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

**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