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Integrate the ordinary differential equation $dy/dx = 2/5$ with respect to x. This yields $y = (2/5)x + c$, where c is an arbitrary constant representing the y-intercept.

Conditions: The ODE is $dy/dx = 2/5$.; c is an arbitrary real constant.

Integrate the ordinary differential equation $dy/dx = 2/5$ with respect to x. This yields $y = (2/5)x + c$, where c is an arbitrary constant representing the y-intercept.

Conditions: The ODE is $dy/dx = 2/5$.; c is an arbitrary real constant.

The slope of the characteristic lines is $2/5$. This is derived from the direction vector (5,2), where the change in y is 2 and the change in x is 5, so $dy/dx = 2/5$.

Conditions: The direction vector is (5,2).; The characteristic lines are straight lines in the xy-plane.

The slope of the characteristic lines is $2/5$. This is derived from the direction vector (5,2), where the change in y is 2 and the change in x is 5, so $dy/dx = 2/5$.

Conditions: The direction vector is (5,2).; The characteristic lines are straight lines in the xy-plane.

u is constant along curves in the direction (5,2) because the directional derivative of u in that direction is zero. If the rate of change of a function is zero in a specific direction, the function's value does not change as one moves along any curve tangent to that direction.

Conditions: (5,2)·∇$u=0$.; The curves considered are tangent to the direction (5,2).

u is constant along curves in the direction (5,2) because the directional derivative of u in that direction is zero. If the rate of change of a function is zero in a specific direction, the function's value does not change as one moves along any curve tangent to that direction.

Conditions: (5,2)·∇$u=0$.; The curves considered are tangent to the direction (5,2).