## Vineet Loomba is teaching live on Unacademy Plus

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)

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!!

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)

FOR 100% SUCCESS IN JEE MAIN AND ADVANCED (11T-JEE) Formation of Differential Equation: The differential equation corresponding to a family of curve can be obtained by using the following steps: Identify the number of essential arbitrary constants in equation of curve. NOTE: If arbitrary constants appear in addition, subtraction, multiplication or division, then we can club them to reduce into one new arbitrary constant. (b) (c) Differentiate the equation of curve till the required order. Eliminate the arbitrary constant from the equation of curve and additional equation obtained in step (b) above. MATHEMATICS FOR IIT-JEE ER. VINEET LOOMBA (IIT RooRKEE)

FOR 100% SUCCESS IN JEE MAIN AND ADVANCED (11T-JEE) Example Form a differential equation of family of straight lines passing through origin Sol. Family of straight lines passing through origin is y = mx where'm'is parameter. Differentiating w.r.t. x dym dx Eliminating 'm' from both equations dy y dx X which is the required differential equation. MATHEMATICS FOR IIT-JEE ER. VINEET LOOMBA (IIT RooRKEE)

FOR 100% SUCCESS IN JEE MAIN AND ADVANCED (IIT-JEE) Example: Form a differential equation of family of circles touching x-axis at the origin? Sol. Equation of family of circles touching x-axis at the origin is where is parameter Eliminating from (i) and (ii) 2xy dy dx X which is required differential equation MATHEMATICS FOR IIT-JEE ER. VINEET LOOMBA (IIT RooRKee)

FOR 100% SUCCESS IN JEE MAIN AND ADVANCED (IIT-JEE) Example: By the elimination of the parameters h and k, find the differential equation of whiclh (x - h)+ (y - k)2- a2, is a solution Solution: Three relations are necessary to eliminate two constants. Thus, besides the given relation, we require two more and they will be obtained by differentiating the given relation twice successively Thus we have)(-) x 0 From (i) and(ii), we obtain dxdx 2 dx and x -h- substituting these values in the given relation, we obtain Which is the required differential equation MATHEMATICS FOR IIT-JEE ER. VINEET LOOMBA (IIT RooRKee)

FOR 100% SUCCESS IN JEE MAIN AND ADVANCED (IIT-JEE) Self Practice Problems 1.Obtain a differential equation of the family of curves y a sin (bx c) where a and c being arbitrary constant 2 2. Show the differential equation of the system of parabolas y2 4a(x - b) is given by 2 dx 3. Find the order of the differential equation of all tangent lines to the parabola y 4 x2. (Ans 1) Form a differential equation of family of parabolas with focus origin and axis of symmetry along the x-axis 2 MATHEMATICS FOR IIT-JEE ER. VINEET LOOMBA (IIT RooRKee)

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)