Let k be real constant. The solution of the differential equations satisfies the relation
Find the General Solution of the given differential equation.
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Consider the differential equation 2 cos (y2)dx - xy sin (y2)dy = 0
If the general solutions of a differential equation are (y + c)2 = cx, where c is an arbitrary constant, then the order and degree of differential equation is
The general solution of
(Here c1 and c2 are arbitrary constants.)
Let y1(x) and y2(x) be linearly independent solution of the differential equation y" + P(x) y' + Q(x)y = 0, where P(x) and Q(x) are continuous functions on an interval I. Then y3(x) = ay1(x) + by2(x) and y4(x) = cy1(x) dy2(x) are linearly independent solutions of the given differential equations if
Consider the differential equations, satisfying y(0) = 0, where This initial value problem
The particular integral of the differential equation
y" + y' + 3y = 5 cos(2x + 3) is
The general solution of differential equation
4x2y" - 8xy' + 9y = 0 is
What is the order of the non-homogeneous partial differential equation,
If g(x, y)dx + (x + y )dy = 0 is an exact differential equation and if g(x, 0) = x2, then the general solution of the differential equation is
Consider the differential equation dy/dx = ay - by2, where a, b > 0 and y(0) = y0. As x → + ∝, the solution y (x) tends to
Orthogonal trajectories of the family of curves (x - 1)2 + y2 + 2ax = 0 are the solution of the differential equation
The solution of differential equation represents the family of
Let then sum of degree and order of given ordinary differential equation is
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