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For the following differential equation, find a particular solution satisfying the given condition:
\[x\left( x^2 - 1 \right)\frac{dy}{dx} = 1, y = 0\text{ when }x = 2\]
Concept: General and Particular Solutions of a Differential Equation
Find the integerating factor of the differential equation `xdy/dx - 2y = 2x^2` .
Concept: Methods of Solving First Order, First Degree Differential Equations >> Linear Differential Equations
Solve the differential equation: (1 +x2 ) dy + 2xy dx = cot x dx
Concept: Methods of Solving First Order, First Degree Differential Equations >> Linear 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
Solve the differential equation: (1 + x2) dy + 2xy dx = cot x dx
Concept: Solutions of Linear Differential Equation
Find the area of the region bounded by the curves (x -1)2 + y2 = 1 and x2 + y2 = 1, using integration.
Concept: Procedure to Form a Differential Equation that Will Represent a Given Family of Curves
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
Solve the differential equation: `(d"y")/(d"x") - (2"x")/(1+"x"^2) "y" = "x"^2 + 2`
Concept: General and Particular Solutions of a Differential Equation
Solve the differential equation: ` ("x" + 1) (d"y")/(d"x") = 2e^-"y" - 1; y(0) = 0.`
Concept: General and Particular Solutions of a Differential Equation
Solve the differential equation : `"x"(d"y")/(d"x") + "y" - "x" + "xy"cot"x" = 0; "x" != 0.`
Concept: Solutions of Linear Differential Equation
Solve the differential equation : `("x"^2 + 3"xy" + "y"^2)d"x" - "x"^2 d"y" = 0 "given that" "y" = 0 "when" "x" = 1`.
Concept: General and Particular Solutions of a Differential Equation
Form the differential equation representing the family of curves y = A sin x, by eliminating the arbitrary constant A.
Concept: Procedure to Form a Differential Equation that Will Represent a Given Family of Curves
Solve the following differential equation :
`"dy"/"dx" + "y" = cos"x" - sin"x"`
Concept: Solutions of Linear Differential Equation
Solve the differential equation `"dy"/"dx" = 1 + "x"^2 + "y"^2 +"x"^2"y"^2`, given that y = 1 when x = 0.
Concept: Methods of Solving First Order, First Degree Differential Equations >> Differential Equations with Variables Separable Method
Find the particular solution of the differential equation `"dy"/"dx" = "xy"/("x"^2+"y"^2),`given that y = 1 when x = 0
Concept: Differential Equations
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: Methods of Solving First Order, First Degree Differential Equations >> Homogeneous Differential Equations
Solve the differential equation: `(1 + x^2) dy/dx + 2xy - 4x^2 = 0,` subject to the initial condition y(0) = 0.
Concept: Methods of Solving First Order, First Degree Differential Equations >> Linear Differential Equations
Solve:
`2(y + 3) - xy (dy)/(dx)` = 0, given that y(1) = – 2.
Concept: General and Particular Solutions of a Differential Equation
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
