For each of the following differential equations

MATHEMATICS · Multi-part · CBSE · Mathematics · Differential Equations · Differential Equations

Problem

For each of the following differential equations, find the general solution and sketch the family of solution curves. (1)

\frac{dy}{dx}=2x

(2)

\frac{dy}{dx}=y

(3)

\frac{dy}{dx}=\frac{2y}{x}

(4)

\frac{dy}{dx}=\frac{x}{y}

(5)

\frac{dy}{dx}=\cos x

(6)

\frac{dy}{dx}=y\cot x,\quad 0<x<\pi