Match List-I with List-II
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List-I |
List-II |
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(A) Integrating factor of $xdy-(y + x^2)dx = 0$ |
(I) $x^2$ |
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(B) Integrating factor of $xdy + (2y + x^2)dx = 0$ |
(II) $x^3$ |
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(C) Integrating factor of $(3y-x^2)dx + xdy = 0$ |
(III) $x$ |
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(D) Integrating factor of $(y + 3x^2)dx + xdy = 0$ |
(IV) $\frac{1}{x}$ |
Choose the correct answer from the options given below:
Answer & explanation
Correct answer: option 1
The correct answer is Option (1) → (A)-(IV), (B)-(I), (C)-(II), (D)-(III)
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List-I |
List-II |
|
(A) Integrating factor of $xdy-(y + x^2)dx = 0$ |
(IV) $\frac{1}{x}$ |
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(B) Integrating factor of $xdy + (2y + x^2)dx = 0$ |
(I) $x^2$ |
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(C) Integrating factor of $(3y-x^2)dx + xdy = 0$ |
(II) $x^3$ |
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(D) Integrating factor of $(y + 3x^2)dx + xdy = 0$ |
(III) $x$ |
(A) x dy − (y + x²) dx = 0
⇒ dy/dx = (y + x²)/x
⇒ dy/dx − (1/x)y = x
Integrating factor (IF) = e^(∫ −1/x dx) = 1/x
⇒ (A) → (IV)
(B) x dy + (2y + x²) dx = 0
⇒ dy/dx = −(2y + x²)/x
⇒ dy/dx + (2/x)y = −x
IF = e^(∫ 2/x dx) = x²
⇒ (B) → (I)
(C) (3y − x²) dx + x dy = 0
⇒ dy/dx = −(3y − x²)/x
⇒ dy/dx + (3/x)y = x
IF = e^(∫ 3/x dx) = x³
⇒ (C) → (II)
(D) (y + 3x²) dx + x dy = 0
⇒ dy/dx = −(y + 3x²)/x
⇒ dy/dx + (1/x)y = −3x
IF = e^(∫ 1/x dx) = x
⇒ (D) → (III)