Problem 07
$y' = x \exp (y - x^2)$, when $x = 0$, $y = 0$.
Solution 07
$\dfrac{dy}{dx} = x e^{y - x^2}$
Problem 05
$2y \, dx = 3x \, dy$, when $x = -2$, $y = 1$.
Solution 05
From Solution 04,
$\dfrac{x^2}{y^3} = c$
Problem 03
$xy \, y' = 1 + y^2$, when $x = 2$, $y = 3$.
Solution 03
$xy \, y' = 1 + y^2$
$xy \dfrac{dy}{dx} = 1 + y^2$
Problem 02
$2xy \, y' = 1 + y^2$, when $x = 2$, $y = 3$.
Solution 2
$2xy \, y' = 1 + y^2$
$2xy \dfrac{dy}{dx} = 1 + y^2$
Problem 04
$2y \, dx = 3x \, dy$, when $x = 2$, $y = 1$.
Solution 04
$2y \, dx = 3x \, dy$
$\dfrac{2y \, dx}{xy} = \dfrac{3x \, dy}{xy}$
Separation of Variables
Homogeneous Functions
Equations with Homogeneous Coefficients
Exact Equations
Linear Equations of Order One
Problem 340
For the system of pulleys shown in Fig. P-340, determine the ratio of W to P to maintain equilibrium. Neglect axle friction and the weights of the pulleys.
Problem 339
The differential chain hoist shown in Fig. P-339 consists of two concentric pulleys rigidly fastened together. The pulleys form two sprockets for an endless chain looped over them in two loops. In one loop is mounted a movable pulley supporting a load W. Neglecting friction, determine the maximum load W that can just be raised by a pull P supplied as shown.
Quadratic Equation
Quadratic equation is in the form
Where
a, b, & c = real-number constants
a & b = numerical coefficient or simply coefficients
a = coefficient of x2
b = coefficient of x
c = constant term or simply constant
a cannot be equal to zero while either b or c can be zero
