1. The problem statement, all variables and given/known data The tangent of any point that belongs to a curve, cuts Y axis in such a way, that the cut off segment in Y axis is twice as big as the X value of the point. Find the equation of the curve, if point (1,4) is part of it. 2. Relevant equations The ultimate solution is [itex]y = x(4-lnx^2)[/itex] 3. The attempt at a solution This might be a little confusing, so I'll try to clarify the situation: assuming for example, that point (1,4) is part of the curve, if we try to find the tangent of the curve at that point, we know that it will cut Y axis where y=2x=2. So in that case the tangent is a line going through (1,4) and (0,2). I guess we get [itex]y = x(4-lnx^2)[/itex] when we put x=1 and y=4 into the general solution, which gives us the specific constant value, then insert the constant value into the general solution to get the final solution. But I don't know how to obtain the general solution. Could you please help me solve this problem?