Amit M Agarwal Solutions for Chapter: Differential Equations, Exercise 5: Work Book Exercise 12.5

The equation of the curve whose tangent at any point $(x, y)$ makes an angle ${\tan }^{-1}(2x+3y)$ with $X$-axis and which passes through $(1,2),$ is

A curve having the condition that the slope of tangent at some point is two times the slope of the straight line joining the same point to the origin of coordinates, is a/an

The equation of the curve satisfying the differential equation $y_2\left(x^2+1\right)=2x{y}_1$ passing through the point $(0,1)$ and having slope of tangent at $x=0$ as $3$, is

The equation of the curve whose sub-normal is equal to a constant $a$, is

The slope at any point of a curve $y=f\left(x\right)$ is given by $\frac{dy}{dx}=3x^2$ and it passes through $(-1,1)$ The equation of the curve is

The curve from which the length of normal is equal to the radius vector, is

The curve for which the intercept cut-off by any tangent on $Y$ -axis is proportional to the square of the ordinate of the point of tendency, is