Embibe Experts Solutions for Chapter: Differential Equations, Exercise 1: EXERCISE-1

The general solution of the differential equation $\frac{dy}{dx}=\frac{1-x}{y}$ is a family of curves which looks most like which of the following?

The solution to the differential equation $y\ln y+x{y}^{\text{'}}=0$, where $y\left(1\right)=e$, is -

The equation of the curve passing through origin and satisfying the differential equation $\frac{dy}{dx}=\sin \left(10x+6y\right)$ is -

The solution of the differential equation $\left(2x-10y^3\right)\frac{dy}{dx}+y=0$ is

Solution of differential equation $\left(1+y^2\right)dx+\left(x-e^{{\tan }^{-1}y}\right)dy=0$ is -

The solution of the differential equation, $e^x\left(x+1\right)dx+\left(y{e}^y-x{e}^x\right)dy=0$ with initial condition $y\left(0\right)=0$, is

The solution of $y^{5}x+y-x\frac{dy}{dx}=0$ is

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