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Differential equations Step by Step

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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
- 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

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
```
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.

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