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Determine the order and degree of the following differential equation:
`[1 + (dy/dx)^2]^(3/2) = 8(d^2y)/dx^2`
Concept: Order and Degree of a Differential Equation
Obtain the differential equation by eliminating the arbitrary constants from the following equation:
y = A cos (log x) + B sin (log x)
Concept: Formation of Differential Equations
Solve the following differential equation:
cos x . cos y dy − sin x . sin y dx = 0
Concept: Formation of Differential Equations
Solve the following differential equation:
`(cos^2y)/x dy + (cos^2x)/y dx` = 0
Concept: Formation of Differential Equations
Solve the following differential equation:
(x2 + y2)dx - 2xy dy = 0
Concept: Formation of Differential Equations
Solve the following differential equation:
`x * dy/dx - y + x * sin(y/x) = 0`
Concept: Methods of Solving First Order, First Degree Differential Equations >> Homogeneous Differential Equations
Solve the following differential equation:
`x^2. dy/dx = x^2 + xy + y^2`
Concept: Methods of Solving First Order, First Degree Differential Equations >> Homogeneous Differential Equations
Solve the following differential equation:
(x2 – y2)dx + 2xy dy = 0
Concept: Methods of Solving First Order, First Degree Differential Equations >> Homogeneous Differential Equations
Solve the following differential equation:
`dy/dx + y/x = x^3 - 3`
Concept: Methods of Solving First Order, First Degree Differential Equations >> Linear Differential Equations
Solve the following differential equation:
`"x" "dy"/"dx" + "2y" = "x"^2 * log "x"`
Concept: Methods of Solving First Order, First Degree Differential Equations >> Linear Differential Equations
Solve the following differential equation:
dr + (2r cotθ + sin2θ)dθ = 0
Concept: Methods of Solving First Order, First Degree Differential Equations >> Linear Differential Equations
In a certain culture of bacteria, the rate of increase is proportional to the number present. If it is found that the number doubles in 4 hours, find the number of times the bacteria are increased in 12 hours.
Concept: Application of Differential Equations
If a body cools from 80°C to 50°C at room temperature of 25°C in 30 minutes, find the temperature of the body after 1 hour.
Concept: Application of Differential Equations
The differential equation `y dy/dx + x = 0` represents family of ______.
Concept: Differential Equations
The integrating factor of linear differential equation `x dy/dx + 2y = x^2 log x` is ______.
Concept: Formation of Differential Equations
The general solution of `(dy)/(dx)` = e−x is ______.
Concept: Formation of Differential Equations
Select and write the correct alternative from the given option for the question
Differential equation of the function c + 4yx = 0 is
Concept: Differential Equations
Select and write the correct alternative from the given option for the question
The order and degree of `(("d"y)/("d"x))^3 - ("d"^3y)/("d"x^3) + y"e"^x` = 0 are respectively
Concept: Order and Degree of a Differential Equation
Select and write the correct alternative from the given option for the question
The solution of `("d"y)/("d"x)` = 1 is
Concept: Formation of Differential Equations
State the degree of differential equation `e^((dy)/(dx)) + (dy)/(dx)` = x
Concept: Order and Degree of a Differential Equation
