Embibe Experts Solutions for Exercise 5: Assignment Set-2

The differential equation $ydy+xdx=dx$ represents

If $\frac{dP}{dy}=3^{\cos y}\sin y,$ then $P$ is equal to

The solution of differential equation $\left(1+x^2\right)\frac{dy}{dx}+y=e^{{\tan }^{-1}x}$ is

A differentiable function $y\left(x\right)$ in $(0,\pi )$ satisfying $y^{\text{'}}=1+y^2,y\left(0\right)=0=y\left(\pi \right)$, is

The differential equation for which ${\sin }^{-1}x+{\sin }^{-1}y=1$, is

If ${\int }_a^{x}ty\left(t\right)dt=x^2+y\left(x\right)$, then $y\left(x\right)=\lambda -\left(\lambda +a^2\right)e^{\frac{x^2-a^2}{\lambda }}$, where $\lambda$ is a natural number then $5^{\lambda }$ is equal to

If the function $y=e^{4x}+2e^{-x}$ is a solution of the differential equation $\frac{d^{3}y}{d{x}^3}-13\frac{dy}{dx}-ky=0$, then $k$ is equal to

The solution of $y^{4}dx+2x{y}^{3}dy=\frac{ydx-xdy}{x^3{y}^3}$ is $x^a{y}^b+k\ln \frac{y}{x}=$ constant, where $a, b$ and $k$ are natural numbers then $(a+b+k)$ is