Question

Solve : (9x + 5y - 9) dx + (5x + 7y - 4) dy = 0​

Answer 1

The required solution is

$\displaystyle \bf 9 {x}^{2} + 10xy + 7 {y}^{2} - 18x - 8y = c$

Given :

$\displaystyle \sf (9x + 5y - 9) dx + (5x + 7y - 4) dy = 0$

To find :

To solve the differential equation

Solution :

Step 1 of 2 :

Write down the given differential equation

Here the given differential equation is

$\displaystyle \sf (9x + 5y - 9) dx + (5x + 7y - 4) dy = 0$

Step 2 of 2 :

Solve the differential equation

$\displaystyle \sf (9x + 5y - 9) dx + (5x + 7y - 4) dy = 0$

$\displaystyle \sf{ \implies }9xdx + 5ydx + 5xdy + 7ydy - 9dx - 4dy = 0$

$\displaystyle \sf{ \implies }9xdx + 5(ydx + xdy) + 7ydy - 9dx - 4dy = 0$

$\displaystyle \sf{ \implies }9xdx + 5d(xy) + 7ydy - 9dx - 4dy = 0$

On integration we get

$\displaystyle \sf{ } \int 9xdx + \int5d(xy) + \int 7ydy -\int 9dx - \int 4dy = 0$

$\displaystyle \sf{ \implies } 9\int xdx + 5\int d(xy) + 7\int ydy -9\int dx - 4\int dy = 0$

$\displaystyle \sf{ \implies }9. \frac{ {x}^{2} }{2} + 5xy + 7. \frac{ {y}^{2} }{2} - 9x - 4y = \frac{c}{2}$

$\displaystyle \sf{ \implies }9 {x}^{2} + 10xy + 7 {y}^{2} - 18x - 8y = c$

Where c is integration constant

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Answer 2

Answer:

Step-by-step explanation: