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Homogenous Differential Equations
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This lesson discusses the concept of homogeneous Differential form

Vineet Loomba is teaching live on Unacademy Plus

Vineet Loomba
IITian | No. 1 Educator in IIT-JEE | 6 Million Minutes Watch Time | 8+ Years Experience | Youtube: Maths Wallah | vineetloomba.com

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Unacademy user
add more lesson mam...your course is very useful... thanks a lot
Pratibha Singh
2 years ago
Tell me Topic
Ritik Kumar
2 years ago
mensuration high level...specifically prism and pyramid....
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Siddharth
2 years ago
hi mam, very useful lesson
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Siddharth
2 years ago
please upload some more useful lesson
Vipul singh
2 years ago
MENSURATION 3D
Udayakiran s
2 years ago
hi mam prepare videos on trigonometry and algebra for ssc cgl beginners
Neetu Singh
2 years ago
Mam plz make lessons on active and passive
Devashish Latwal
2 years ago
Ma'am can you please create a course on geometry
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Priyanka ora
2 years ago
Hello mam very nice series of lectures. plz upload profit & loss problems
Hello Vineet, this very informative course, I have gone through many of your courses. all the courses were very very informative. please can you tell us how could we download this lec in pdf or ppt form? thanks!
  1. DIFFERENTIAL EqUATIONS (DETAILED COURSE) JEE MAIN AND ADVANCED IIT-IEE MATHS MADE EASY PREPARED BY: ER. VINEET LOOMBA IITiAN | IIT-JEE MENTOR FoR SURE SHoT SUcCESS IN JEE MAIN AND ADVANCED (IIT-JEE)


  2. FOR 100% SUCCESS IN JEE MAIN AND ADVANCED (IIT-JEE) ABOUT ME B.Tech. From IIT Roorkee -$ IIT-JEE Mentor Since 2010. -^ Doubts/Feedback in Comment Section * Comment other topics you want to revise. * Follow me @ https://unacademy.com/user/vineetloomba to get unacademy updates or search me on Google * Share among your peers as SHARING is CARING!!


  3. FOR 100% SUCCESS IN JEE MAIN AND ADVANCED (IIT-JEE) Other Detailed Courses Made so far on Unacademv: V Strategy for JEE Main and Advanced V Sets, Relations and Functions V Trigonometry V Applications of Derivatives Limits, Continuity. Differentiability V Indefinite Integration V Definite Integration V Complex Number V Logarithmic Functions V Sequences Series V Most Important Questions in IIT-JEE Permutations Combinations V Binomial Theorem V Straight Lines V Applications of Integrals V Circles (Detailed Course) V Probability MathematicS V Parabola (Detailed Course) v Inverse Trigonometry V Mathematical Reasoning V Ellipse (Detailed Course) V Hyperbola Upcoming Courses next month: Coordinate Geometry > Differential Equations Differential Equations MATHEMATICS FOR IIT-JEE ER. VINEET LOOMBA (IIT RooRKee)


  4. FOR 100% SUCCESS IN JEE MAIN AND ADVANCED (IIT-JEE) dy 2x y +2 dx 2y- 4x +1 Example: Sove the differential equation dy dx 2x -y +2 2y- 4x +1 Solution: We have dy 2x - y+2 Here and a 42 2 2 dy (2x y)+2 0 dx 2(2x-y)+1 dz dx dy dx dy dz dx Let z = 2x-y 221dz-dx (variables are separate) 2z -1 dz 5z Integrating both sides, we get 5 5z 22-log Izl = 5x + 5C 2(2x-y) _ log 12x-yl = 5x + C, where C, = 5C MATHEMATICS FOR IIT-JEE ER. VINEET LOOMBA (IIT RooRKee)


  5. FOR 100% SUCCESS N JEE MAIN AND ADVANCED (IIT-JEE) Homogeneous Differential Equations: dy f(x,y) A differential equation of the from dxgx.y) dx g(x,y) where f and g are homogeneous function of x and y, and of the same degree, is called homogeneous differential equation and can be solved easily by putting MATHEMATICS FOR IIT-JEE ER. VINEET LOOMBA (IIT RooRKEE)


  6. FOR 100% SUCCESS IN JEE MAIN AND ADVANCED (IIT-JEE) Example: Solve x dy-ydx-VX2-y2 dx = 0 Solution: We have Which is a homogeneous equation. Using the transformation equation (i) reduces to dx dv .e x dv V1-V2 in which the variables are separated. Integrating, we have sin 1 v In xIn C (arbitrary constant) sin-111-h(Cx) ie. which is the required solution MATHEMATICS FOR IIT-JEE ER. VINEET LOOMBA (IIT RooRKee)


  7. FOR 100% SUCCESS IN JEE MAIN AND ADVANCED (IIT-JEE) Solve 2 Y dy dx Example Solution. Putting y=vx dy 2v 2 dv dx 2v 1 1+v2 v x2+y2=yc' where c'=ec MATHEMATICS FOR IIT-JEE ER. VINEET LOOMBA (IIT RooRKee)


  8. FOR 100% SUCCESS IN JEE MAIN AND ADVANCED (IIT-JEE) Example Solve : (x2- ) dx 2xydy 0 given that y-1 when x 1 2 2 Solution. y=VX dy dx 2xy dv dv at MATHEMATICS FOR IIT-JEE ER. VINEET LOOMBA (IIT RooRKee)


  9. FOR 100% SUCCESS IN JEE MAIN AND ADVANCED (IIT-JEE) Practice Problems Ans: x2(y2 +2xy) -c y tan-1 x given that y 0 atx- 1 dx 2 , 2 dy Ans: y=ce'x ylx dx dx xdx=y-xtan MATHEMATICS FOR IIT-JEE ER. VINEET LOOMBA (IIT RooRKee)


  10. FOR 100% SUCCESS N JEE MAIN AND ADVANCED (IIT-JEE) ENROL for this Course (Free) Enroll 439 Recommend Lessons (Like) E Rate and Review the Course .Comments . Sharing with friends 15 68 111 ratings 21 reviews Share MATHEMATICS FOR IIT-JEE ER. VINEET LOOMBA (IIT RooRKEE)