Embibe Experts Solutions for Chapter: Differential Equations, Exercise 2: Level 2

Let $y=f\left(x\right)$ be a curve which passes through $\left(3,1\right)$ and is such that normal at any point on it passes through $\left(1,1\right)$. Then, $y=f\left(x\right)$ describes

The general solution of the differential equation $\frac{dy}{dx}+\sin \left(\frac{x+y}{2}\right)=\sin \left(\frac{x-y}{2}\right)$

The equation of the curve passing through the point $\left(0,\frac{\pi }{4}\right)$ and satisfying the differential equation $\left(e^x\tan y\right)dx+\left(\left(1+e^x\right){\sec }^{2}y\right)dy=0$ is given by

The general solution of $\frac{dy}{dx}=x+\sin x\cos y+x\cos y+\sin x$ is

If $y=y\left(x\right)$ is the solution of the equation $e^{\sin y}\cos y\frac{dy}{dx}+e^{\sin y}\cos x=\cos x, y\left(0\right)=0$; then $1+y\left(\frac{\pi }{6}\right)+\frac{\sqrt{3}}{2}y\left(\frac{\pi }{3}\right)+\frac{1}{\sqrt{2}}y\left(\frac{\pi }{4}\right)$ is equal to _______.

Solution of the differential equation $\sin 2x\frac{dy}{dx}-y=\tan x$ 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

If the curve, $y=y\left(x\right)$ represented by the solution of the differential equation $\left(2x{y}^2-y\right)dx+x dy=0$, passes through the intersection of the lines, $2x-3y=1$ and $3x+2y=8$, then $\left|y\left(1\right)\right|$ is equal to ___ .