K. C. Sinha Solutions for Chapter: Differential Equations - II, Exercise 3: EXERCISE

The solution of the equation $\frac{dy}{dx}=x^3 y^2+xy$ is

A tangent drawn to the curve $y=f\left(x\right)$ at $P(x,y)$ cuts the $x$-axis and $y$-axis at $A$ and $B$, respectively, such that $BP:AP=3:1$. Given that $f\left(1\right)=1$, then

For the differential equation $(x^2+y^2)dx-2xy dy=0$, which of the following are true.

The curve represented by the differential equation $(x^2+y^2+1)dx-2xy dy=0$ satisfying $y\left(1\right)=1$ is

The curve represented by the differential equation $\cos y(1-x\cos y)dx-\sin y dy=0$ satisfying $y\left(0\right)=0$ is

Which of the following are true for the differential equation $\frac{dy}{dx}-\frac{y}{x}+\frac{5x}{(x+2)(x-3)}=0$, if the curve represented by it passes through the point $\left(5,a\log \frac{7}{12}\right)$, where $a$ is a natural number.

Which of the following are true for the curve represented by the differential equation ${\sec }^{2}y\frac{dy}{dx} +2x\tan y=x^3$ satisfying $y\left(1\right)=0$.

A curve $y=f\left(x\right)$ satisfies $\frac{d^{2}y}{d{x}^2}= 6x- 4$ and $f\left(x\right)$ has local minimum value $5$ at $x=1$. If $a$ and $b$ be the global maximum and global minimum values of $f\left(x\right)$ in interval $[0,2]$, then $ab$ is equal to