Question

Solve the partial differential equation : r – 4s + 4t = 0.​

Answer 1

Answer:

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Step-by-step explanation:

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Answer 2

Step-by-step explanation:

Given:

The partial differential equation $r-4s+4t=0.$

To find:

The solution of the partial differential equation $r-4s+4t=0.$

Solution:

Given that,

$r-4s+4t=0$

Subtract $r$ from both sides of the equation.

⇒ $r-4s+4t-r=0-r$

⇒ $-4s+4t+0=0-r$

Here anything subtracted from zero gives its negation.

⇒ $-4s+4t=-r$

Now subtract $4t$ from both sides of the equation.

⇒ $-4s+4t-4t=-r-4t$

⇒ $-4s+0=-r-4t$

⇒ $-4s=-r-4t$

Divide both sides by $-4.$

⇒ $\frac{-4s}{-4} =\frac{-r-4t}{-4}$

Dividing $-4$ undoes the multiplication by $-4$.

⇒ $s=\frac{-r-4t}{-4}$

Divide $-r-4t$ by $-4.$

⇒ $s=\frac{(-r+4)}{-4}$

⇒ $s=\frac{r+4t}{4}$ or $s=\frac{r}{4} +t$

Answer:

The solution of the partial differential equation $r-4s+4t=0$ is $s=\frac{r+4t}{4}.$