## 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) Differential Equation: An equation involving independent and dependent variables and the derivatives of the dependent variables is called a differential equation. There are two kinds of differential equation MATHEMATICS FOR IIT-JEE ER. VINEET LOOMBA (IIT RooRKEE)

FOR 100% SUCCESS IN JEE MAIN AND ADVANCED (IIT-JEE) Ordinary Differential Equation If the dependent variables depend on one independent variable x, then the differential equation is said to be ordinary dy dz for example + Xy sin X , dx 3/2 2 2 dx dx MATHEMATICS FOR IIT-JEE ER. VINEET LOOMBA (IIT RooRKee)

FOR 100% SUCCESS IN JEE MAIN AND ADVANCED (11T-JEE) Partial differential equation If the dependent variables depend on two or more independent variables, then it is known as partial differential equation 2 for example y2_+y--ax,-+--0 2 MATHEMATICS FOR IIT-JEE ER. VINEET LOOMBA (IIT RooRKEE)

FOR 100% SUCCESS IN JEE MAIN AND ADVANCED (IIT-JEE) Order: Order is the highest differential appearing in a differential equation. Degree : It is determined by the degree of the highest order derivative present in it after the differential equation is cleared of radicals and fractions so far as the derivatives are con- cerned 2 dmy f,(x, y) dX The above differential equation has the order m and degree n- MATHEMATICS FOR IIT-JEE ER. VINEET LOOMBA (IIT RooRKee)

FOR 100% SUCCESS IN JEE MAIN AND ADVANCED (11T-JEE) Example: 2 6 71/4 dy ( dx 4 d-y dx dy dx :. order 2, degree4 MATHEMATICS FOR IIT-JEE ER. VINEET LOOMBA (IIT RooRKEE)

FOR 100% SUCCESS IN JEE MAIN AND ADVANCED (11T-JEE) Example: dx dx" y- 2 dx dx . order 2, degree 1 2 MATHEMATICS FOR IIT-JEE ER. VINEET LOOMBA (IIT RooRKEE)

FOR 100% SUCCESS IN JEE MAIN AND ADVANCED (11T-JEE) Example: dy dy Sin dx dx2 day 2 + dy = sin-1 y dx2 dx order 2, degree -1 MATHEMATICS FOR IIT-JEE ER. VINEET LOOMBA (IIT RooRKEE)

FOR 100% SUCCESS IN JEE MAIN AND ADVANCED (IIT-JEE) Self Practice Problems: Find order and degree of the following differential equations. Ans. order 1, degree 2 ja. dy dy dx d = (n ( + 11 y5Ans. order 5, degree not applicable order dx5 1/2 Ans" order = 2, degree = 2 MATHEMATICS FOR IIT-JEE ER. VINEET LOOMBA (IIT RooRKee)