Question

The general solution of 2p + 3q = a is given by
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Answer 1

Answer:

5p

Step-by-step explanation:

as the math you are asking a hard question but it is 5p because we consider higher number

Answer 2

The general solution of 2p + 3q = a is ϕ ( 3x − 2y, ay − 3z)=0.

Given:

The equation 2p + 3q = a.

To Find:

The general solution of the given equation.

Solution:

The given partial differential equation can be written as

Pp+ Qq = R where P = 2, Q = 3, and R = a.

Lagrange’s auxiliary equations are given by

$\frac{dx}{2}$ = $\frac{dy}{3}$ = $\frac{dz}{a}$

Firstly let's take

⇒ $\frac{dx}{2}$ = $\frac{dy}{3}$

⇒ 3dx = 2dy

Now on integrating both sides we get

3x − 2y = $c_{1}$

Next, let us take

$\frac{dy}{3}$  =      $\frac{dz}{a}$

⇒ ady = 3dz

​Now on integrating both sides we get

ay − 3z = $c_{2}$

The required general solution is given by

ϕ ( 3x − 2y, ay − 3z)=0

∴ The general solution of 2p + 3q = a is ϕ ( 3x − 2y, ay − 3z)=0.

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