Show that the given differential equation is homogeneous and solve each of them.(x2−y2)dx+2xydy=0
In a bank, principal increases continuously at the rate of 5% per year. In how many years Rs 1000 double itself?
The general solution of the differential equation yydx−xdy=0is(A) xy=C (B) x=Cy2 (C) y=Cx (D) y=Cx2
Verify that the given functions (explicit or implicit) is a solution of the corresponding differential equation:y=x2+2x+C : yprime−2x−2=0
The general solution of the differential equation exdy+(yex+2x)dx=0is(A) xey+x2=C (B) xey+y2=C (C) yex+x2=C (D) yey+x2=C
Find the particular solution of the differential equation dxdy+ycotx=2x+x2cotx(x=0)given that y=0when x=2π.
Form the differential equation representing the family of ellipses having foci on x-axis and centre at the origin.
Find the equation of a curve passing through the point (2,3), given that the slope of the tangent to the curve at any point (x, y) is y22x.