## Problem 04 | Determination of Integrating Factor

**Problem 04**

$y(4x + y)~dx - 2(x^2 - y)~dy = 0$

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**Problem 04**

$y(4x + y)~dx - 2(x^2 - y)~dy = 0$

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**Problem 03**

$y(2x - y + 1)~dx + x(3x - 4y + 3)~dy = 0$

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**Problem 02**

$2y(x^2 - y + x)~dx + (x^2 - 2y)~dy = 0$

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**Problem 01**

$(x^2 + y^2 + 1)~dx + x(x - 2y)~dy = 0$

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Problem 04 | Exact Equations

**Problem 04**

$(y^2 - 2xy + 6x) \, dx - (x^2 - 2xy + 2) \, dy = 0$

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Problem 03 | Exact Equations

**Problem 03**

$(2xy - 3x^2) \, dx + (x^2 + y) \, dy = 0$

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Problem 02 | Exact Equations

**Problem 02**

$(6x + y^2) \, dx + y(2x - 3y) \, dy = 0$

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Problem 01 | Exact Equations

**Problem 01**

$(x + y) \, dx + (x - y) \, dy = 0$

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01 Maximum area of triangle of given perimeter

**Problem 1**

Show that the largest triangle of given perimeter is equilateral.

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**Problem**

A gutter whose cross-section is trapezoidal is to be made of galvanized iron sheet of 24 m wide. If its carrying capacity is maximum, find the dimension of the base.

A. 4 m

B. 6 m

C. 8 m

D. 10 m

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