The solution of the differential equation yy' + y2 - x = 0, where c is a constant, is
Let k be a real constant. The solution of the differential equations satisfies the relation
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If general solution of the differential equation ay",+ by"- cy’+ dy = 0 is linearly spanned by ex sin x and cos x, then which one of the following holds?
Two linearly independent solutions of the differential equation y" - 2y' + y = 0 are y1 = ex and y2 = xex. Then a particular solution of y"- 2y' + y + ex sin x is
Orthogonal trajectories of the family of curves (x - 1)2 + y2 + 2ax = 0 are the solutions of the differential equation
Which one of the following differential equations represents all circles with radius a?
The solution of the differential equation with initial condition y(0) = 0 is
The differential equation (2a2 + by2) dx + cxydy = 0 is made exact by multiplying the integrating factor Then the relation between b and c is.
The sum of the intercepts made on the axes of co-ordinates by any tangent to the curve √x + √y = 2 is equal to
If and it is known that for x = 1, y = 1; if x = -1, then the value of y will be :
If the solution of the differential equation is x + y -1 = Ceu then the value of u is :
The degree and order of differential equation are respectively
The solution of the equation (2x + y + 1)dx + (4x + 2y – 1)dy = 0 is:
The solution of the differential equation y(x2y + ex)dx- exdy = 0 is