x^2y2-2x(1+x)y1+2(1+x)y=x^3 скачать в хорошем качестве

x^2y2-2x(1+x)y1+2(1+x)y=x^3

#explanationinenglish #reductionoforder #mathspulse Hello, People! Here is a video of a differential equation of order two, we will solve this equation using reduction of order method. Please watch with patience and have a happy learning. My heart felt thanks to all the subscribers, audience, supporters and well-wishers❤ With Love, Chinnaiah Kalpana🌷 Note: Working rules to find part of C.F. of d^2y/dx^2+Pdy/dx+Qy=0 by inspection: 1. y=e^x is the part of C.F. if 1+P+Q=0. 2. y=e^-x is the part of C.F. if 1-P+Q=0. 3. y=e^ax is the part of C.F. if a^2+Pa+Q=0. 4. y=x^m is the part of C.F. if m(m-1)+Pmx+Qx^2=0. 5. y=x is the part of C.F. if P+Qx=0. 6. y=x^2 is the part of C.F. if 2+2Px+Qx^2=0. Working rule to solve d^2y/dx^+Pdy/dx+Qy=R 1. Reduce the given equation to standard form as d^2y/dx^2+Pdy/dx+Qy=R-----(1) 2. Either a part of C.F. is given or it can be found by inspection in some cases given above. Let it be y=u. 3. Let y=uv be the general solution of (1) where v=f(x) 4. Then dy/dx = u.dv/dx+v.du/dx and d^2y/dx^2=u.d^2v/dx^2+(du/dx)(dv/dx) +(du/dx)(dv/dx)+vd^2v/dx^2 =vd^2u/dx^2+2du/dcdv/dx+ud^2v/dx^2 5. With these substitutionsin(1), takes the form: d^2v/dx^2+P1 dv/d=R1 where P1=P+2/u du/dx nd R1 = R/u 6. Taking dv/dx=V, it becomes dV/dx+P1 V=R1 which is a linear in V and x and hence it can be solved for V. 7. V=dv/dx on integration gives v. 8. Then the required general solution is y=uv. " But in our problem, we are finding v directly using the equation d^2v/dx^2+[P+2/u du/dx]dv/dx = R/u". For more such videos👇    • Higher Order Linear Differential Equations   Find me on Instagram 🌼   / mathspulse_chinnaiahkalpana   Stay tuned to 'Maths Pulse'. Get rid of 'Maths Phobia'. Have a happy learning! #chinnaiahkalpana #differenialequations #engineeringmathematics #bscmaths #math #differentialequationwithnonconstantcoefficients #problemsonreductionoforder