Q. 85.0( 1 Vote )

# Solve the following equations:

Answer :

Given Differential equation is:

⇒

⇒ ……(1)

Homogeneous equation: A equation is said to be homogeneous if f(zx,zy) = z^{n}f(x,y) (where n is the order of the homogeneous equation).

Let us assume

⇒

⇒

⇒

⇒

⇒ f(zx,zy) = z^{0}f(x,y)

So, given differential equation is a homogeneous differential equation.

We need a substitution to solve this type of linear equation and the substitution is y = vx.

Let us substitute this in (1)

⇒

We know that

⇒

⇒

⇒

⇒

Bringing like variables on same side we get,

⇒

⇒

⇒

We know that:

and

Also,

Integrating on both sides, we get,

⇒

⇒

(∵ log C is an arbitrary constant)

⇒

(∵ alogx = logx^{a})

⇒

(∵ loga + logb = logab)

Since y = vx,

we get,

⇒

⇒

⇒

Applying exponential on both sides we get,

⇒

⇒

∴ The solution of the Differential equation is

Rate this question :

Solve the differential equation :

(tan^{-1}y – x)dy = (1 + y^{2})dx.

**OR**

Find the particular solution of the differential equation given that y = 1, when x = 0.

Mathematics - Board PapersSolve the following differential equation:

Mathematics - Board Papers

Find the particular solution of the differential equation given that when

Mathematics - Board PapersShow that the differential equation (x e^{y/x} + y)dx = xdy is homogeneous. Find the particular solution of this differential equation, given that x = 1 when y = 1.

Solve the differential equation:

given that when

Mathematics - Board PapersFind the particular solution of the following differential equation. given that when x = 2, y = π

Mathematics - Board Papers