Verify that the given functions (explicit or implicit) is a solution of the corresponding differential equation:y=cosx+C : yprime+sinx=0
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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
Statement 1 : Order of a differential equation represents the number of arbitrary constants in the general solution.
Statement 2 : Degree of a differential equation represents the number of family of curves.
Integrating factor of differential equation cosxdxdy+ysinx=1 is
Let the function lnf(x) is defined where f(x) exists for x≥2andk is fixed positive real numbers prove that if dxd(x.f(x))≥−kf(x) then f(x)≥Ax−1−k where A is independent of x.
From the differential equation of family of lines situated at a constant distance p from the origin.
then find y(x)
The curve satisfying the equation dxdy=x(y3−x)y(x+y3) and passing through the point (4,−2) is
Show that the differential equation (x2+xy)dy=(x2+y2)dx is homogenous and solve it.