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Show that the differential equation 2yx/y dx + (y − 2x ex/y) dy = 0 is homogeneous. Find the particular solution of this differential equation, given that x = 0 when y = 1.
Concept: Forms of Solving Differential Equations> Homogeneous Differential Equations
Solve the differential equation :
`y+x dy/dx=x−y dy/dx`
Concept: Forms of Solving Differential Equations> Homogeneous Differential Equations
Show that the differential equation `2xydy/dx=x^2+3y^2` is homogeneous and solve it.
Concept: Forms of Solving Differential Equations> Homogeneous Differential Equations
Which of the following is a homogeneous differential equation?
Concept: Forms of Solving Differential Equations> Homogeneous Differential Equations
Solve the following differential equation:
\[\text{ cosec }x \log y \frac{dy}{dx} + x^2 y^2 = 0\]
Concept: Basic Concepts of Differential Equations
Solve the following differential equation : \[y^2 dx + \left( x^2 - xy + y^2 \right)dy = 0\] .
Concept: Basic Concepts of Differential Equations
Write the sum of the order and degree of the differential equation
\[\left( \frac{d^2 y}{{dx}^2} \right)^2 + \left( \frac{dy}{dx} \right)^3 + x^4 = 0 .\]
Concept: Order and Degree of a Differential Equation
Solve the following differential equation : \[\left[ y - x \cos\left( \frac{y}{x} \right) \right]dy + \left[ y \cos\left( \frac{y}{x} \right) - 2x \sin\left( \frac{y}{x} \right) \right]dx = 0\] .
Concept: Forms of Solving Differential Equations> Homogeneous Differential Equations
Solve the following differential equation : \[\left( \sqrt{1 + x^2 + y^2 + x^2 y^2} \right) dx + xy \ dy = 0\].
Concept: Basic Concepts of Differential Equations
If xmyn = (x + y)m+n, prove that \[\frac{dy}{dx} = \frac{y}{x} .\]
Concept: Basic Concepts of Differential Equations
Write the order and degree of the differential equation `((d^4"y")/(d"x"^4))^2 = [ "x" + ((d"y")/(d"x"))^2]^3`.
Concept: Order and Degree of a Differential Equation
Write the order and the degree of the following differential equation: `"x"^3 ((d^2"y")/(d"x"^2))^2 + "x" ((d"y")/(d"x"))^4 = 0`
Concept: Order and Degree of a Differential Equation
Find the order and the degree of the differential equation `x^2 (d^2y)/(dx^2) = { 1 + (dy/dx)^2}^4`
Concept: Order and Degree of a Differential Equation
Solve the differential equation: x dy - y dx = `sqrt(x^2 + y^2)dx,` given that y = 0 when x = 1.
Concept: Forms of Solving Differential Equations> Homogeneous Differential Equations
The order and degree of the differential equation `[1 + ((dy)/(dx))^2] = (d^2y)/(dx^2)` are ______.
Concept: Order and Degree of a Differential Equation
Write the sum of the order and the degree of the following differential equation:
`d/(dx) (dy/dx)` = 5
Concept: Order and Degree of a Differential Equation
If m and n, respectively, are the order and the degree of the differential equation `d/(dx) [((dy)/(dx))]^4` = 0, then m + n = ______.
Concept: Order and Degree of a Differential Equation
The order and the degree of the differential equation `(1 + 3 dy/dx)^2 = 4 (d^3y)/(dx^3)` respectively are ______.
Concept: Order and Degree of a Differential Equation
If `(a + bx)e^(y/x)` = x then prove that `x(d^2y)/(dx^2) = (a/(a + bx))^2`.
Concept: Order and Degree of a Differential Equation
The degree of the differential equation `[1 + (dy/dx)^2]^3 = ((d^2y)/(dx^2))^2` is ______.
Concept: Order and Degree of a Differential Equation
