Let f:(0,∞)→R be a differentiable function such that f′(x)=2−xf(x) for all x∈(0,∞) and f(1)=1, then
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Consider the equation a2+λx2+b2+λy2=1,
where a and b are specified constants and λ
is an arbitrary parameter. Find a differential equation satisfied by it.
The differential equation representing the family of curves y2=2c(x+c), where c is a positive parameter, is of (A) order 1 (B) order 2 (C) degree 3 (D) degree 4
Find the orthogonal trajectory of y2=4ax
(a being the parameter).
The equation of the curve satisfying xdy−ydx=x2−y2−−−−−−√ and y(1)=0 is:
The general solution of the differential equation dydx−tany1+x=(1+x)exsecy is
The differential equation of the family of circles with fixed radius 5 units and centre on the line y=2 is
Find the curve for which the length of normal is equal to the radius vector.
What is the solution of satisfying?