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x2d2ydx2x22xdydxx2yx3ex Reductionoforder L950
>> YOUR LINK HERE: ___ http://youtube.com/watch?v=XVvuqhfHjuU
#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 Equa... • • • 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
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