Embibe Experts Solutions for Exercise 2: EXERCISE 10.2

The general solution of differential equation $\frac{dy}{dx}=\frac{x+y}{x-y}$ is

Solution of differential equation $\left(2x\cos y+y^2\cos x\right)dx+\left(2y\sin x-x^2\sin y\right)dy=0$ is -

Solution of the differential equation $\left(3x{y}^2+x\sin \left(xy\right)\right)dy+\left(y^3+y\sin \left(xy\right)\right)dx=0$ is

The solution of the differential equation $\left(1+x^2\right)(1+y)dy+(1+x)\left(1+y^2\right)dx=0$ is

The solution of $\frac{dy}{dx}={\left(4x+y+1\right)}^2$ is

The solution of $ydx-xdy+3x^2{y}^2{e}^{x^3}dx=0$ is

The solution of the differential equation $3e^x\tan ydx+\left(1+e^x\right){\sec }^{2}ydy=0$ is

The slope of the tangent at $(x,y)$ to a curve passing through $\left(1,\frac{\mathrm{\pi }}{4}\right)$ is given by $\frac{y}{x}-{\cos }^2\left(\frac{y}{x}\right)$, then the equation of the curve is