x^2d^2y/dx^2+xdy/dx+y=4Sin(logx) #CauchyEulerLinearEquation L902

#explanationinenglish #higherorderlineardifferentialequation Hello, People! Here is a video of solving a differential equation which is of Cauchy's form. By reducing the given Cauchy's equation(linear differential equation with variable coefficient) to linear differential equation with constant coefficient. Watch with patience till end, or skip some part. My hearty thanks to all the subscribers, supporters, viewers and well-wishers💛 With Love, Chinnaiah Kalpana🌞 Note: Cauchy's Homogeneous Linear Differential Equations: an euation of the form a0 x^n D^n y +a1 x^n-1 D^n-1 y + ....+ an-1 x D y +an y =Q(x) where a0, a1,...,an are constants with a0 non zero, is called Cauchy's homogeneous libear differential equation (or) Euler-Cauchy linear equation (or) Euler's linear equation. This can be reduced to a linear differential equation with constant coefficients. Put x = e^z then z = logx dydx =dy/dz dz/dx =dy/dz.1/x then x dy/dx = dy/dz then xD y = θ y then xD=θ X^2D^2 = θ(θ-1) x^3D^3=θ(θ-1)(θ-2) .... Later use known methods to find general solution of the given problem. For more such videos👇👇    • Higher Order Linear Differential Equations   You can also find me on Instagram 🌼   / mathspulse_chinnaiahkalpana   Stay tuned to 'Maths Pulse'. Get rid of 'Maths Phobia'. Have a happy learning! #eulercauchyequation #eulercauchylinearequation #lineardifferentialequationswithvariablecoefficients #higherorderlineardifferentialequationswithnonconstantcoefficients