Question

Solve (3x2 + 4xy)dx +(2x2 + 2y)dy
= 0​

Answer 1

SOLUTION

TO SOLVE

$\sf{(3 {x}^{2} + 4xy)dx + (2 {x}^{2} + 2y)dy = 0 }$

EVALUATION

$\sf{(3 {x}^{2} + 4xy)dx + (2 {x}^{2} + 2y)dy = 0 }$

$\implies \sf{3 {x}^{2}dx + 4xydx + 2 {x}^{2}dy + 2ydy = 0 }$

$\implies \sf{3 {x}^{2}dx + d(2 {x}^{2}y) + 2ydy = 0 }$

Integrating both sides we get

$\displaystyle \sf{3 . \frac{ {x}^{3} }{3} + 2 {x}^{2}y + 2 .\frac{ {y}^{2} }{2} = c }$

$\implies \displaystyle \sf{ {x}^{3} + 2 {x}^{2}y + {y}^{2} = c }$

Where C is integration constant

FINAL ANSWER

The required solution is

$\boxed{ \: \: \displaystyle \sf{ {x}^{3} + 2 {x}^{2}y + {y}^{2} = c } \: \: }$

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Answer 2

Answer:

Step-by-step explanation: