#### Find the general solution of the given differential equation.

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

So the general solution to the differential equation is found by integrating IQ and then re-arranging the formula to make y the subject. x3 dy dx + 3x2y = ex so integrating both sides we have x3y = ex + c where c is a constant. Thus the general solution is y = ex + c x3 .

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

Another way to find a singular solution as the envelope of the family of integral curves is based on using C-discriminant. Let Φ(x,y,C) be the general solution of a differential equation F(x,y,y′)=0. Graphically the equation Φ(x,y,C)=0 corresponds to the family of integral curves in the xy-plane.

## What is general solution and particular solution?

A solution yp(x) of a differential equation that contains no arbitrary constants is called a particular solution to the equation. GENERAL Solution TO A NONHOMOGENEOUS EQUATION. Let yp(x) be any particular solution to the nonhomogeneous linear differential equation. a2(x)y″+a1(x)y′+a0(x)y=r(x).

## What is general solution in trigonometry?

Trigonometric Equations with their general Solutions:

Trigonometrical equation | General Solution |
---|---|

sin θ = 0 | Then θ = nπ |

cos θ = 0 | θ = (nπ + π/2) |

tan θ = 0 | θ = nπ |

sin θ = 1 | θ = (2nπ + π/2) = (4n+1)π/2 |

## What is linear equation in differential equation?

In mathematics, a linear differential equation is a differential equation that is defined by a linear polynomial in the unknown function and its derivatives, that is an equation of the form. where , , and are arbitrary differentiable functions that do not need to be linear, and.

## What is clairaut’s equation of differential equation?

Clairaut’s equation, in mathematics, a differential equation of the form y = x (dy/dx) + f(dy/dx) where f(dy/dx) is a function of dy/dx only. The equation is named for the 18th-century French mathematician and physicist Alexis-Claude Clairaut, who devised it.

## What is particular solution?

: the solution of a differential equation obtained by assigning particular values to the arbitrary constants in the general solution.

## What are the types of differential equations?

We can place all differential equation into two types: ordinary differential equation and partial differential equations. A partial differential equation is a differential equation that involves partial derivatives.

## How do you solve a differential equation with two variables?

Step 1 Separate the variables by moving all the y terms to one side of the equation and all the x terms to the other side:Multiply both sides by dx:dy = (1/y) dx. Multiply both sides by y: y dy = dx.Put the integral sign in front:∫ y dy = ∫ dx. Integrate each side: (y^{2})/2 = x + C.Multiply both sides by 2: y^{2} = 2(x + C)

## What does General solution mean?

1 : a solution of an ordinary differential equation of order n that involves exactly n essential arbitrary constants. — called also complete solution, general integral. 2 : a solution of a partial differential equation that involves arbitrary functions.

## How do you find the general solution and principal solution?

If the equation involves a variable 0 ≤ x < 2π, then the solutions are called principal solutions. A general solution is one which involves the integer 'n' and gives all solutions of a trigonometric equation. Also, the character 'Z' is used to denote the set of integers.