Question
Question: Solution of differential equation (2x cos y + y<sup>2</sup> .cos x)dx + (2y . sin x – x<sup>2</sup>...
Solution of differential equation (2x cos y + y2 .cos x)dx +
(2y . sin x – x2 . sin y)dy = 0 is –
A
x2.cos y + y2 . sin x = C
B
x .cos y – y . sin x = C
C
x2 . cos2 y + y2 . sin2x = C
D
xcos y + y sin x = C
Answer
x2.cos y + y2 . sin x = C
Explanation
Solution
2 x cos y dx + y2 cos x dx + 2y sin x dy – x2 sin y dy = 0
Ž (2 x cos y dx – x2 sin y dy) + (y2 cos x dx + 2y sin x dy) = 0
Ž d(x2 cos y + y2 sin x) = 0
Ž x2 cos y + y2 sin x = C