PYQs Based Test - 14 : Euler-Cauchy Equations

General solution of $x^2\frac{d^{2}y}{d{x}^2}+x\frac{dy}{dx}-y=0$ is

Consider the differential equation $x^2\frac{d^{2}y}{d{x}^2}+x\frac{dy}{dx}-4y=0$ with the boundary conditions of y(0) = 0 and y(1) = 1. The complete solution of the differential equation is

The solution of differential equation $x^2\frac{d^{2}y}{d{x}^2}-2x\frac{dy}{dx}+2y=0$ will be ___________, where c₁ and c₂ are arbitrary constants.

General solution of the Cauchy-Euler equation $x^2\frac{d^{2}y}{d{x}^2}-7x\frac{dy}{dx}+16y=0$ is

A differential equation is given as:

$x^2\frac{d^{2}y}{d{x}^2}-2x\frac{dy}{dx}+2y=4$

The solution of the differential equation in terms of arbitrary constants C₁and C₂ is