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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 (Maths) | 2.6 Million Minutes Watch Time | 8+ Years Experience | Youtube: Maths Wallah | vineetloomba.com

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During a volcanic explosion the top of the cone may be blown off leaving behind a natural hollow called a crater. This may be enlarged by subsidence into a caldera. In dormant or extinct volcanoes, rain falls straight into the crater or caldera which has no superficial outlet and forms a crater or caldera lake. Examples: Lonar in Maharashtra and Krakatao in Indonesia.
  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)