## 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 (IIT-JEE) Linear Differential Equatiorn When the dependent variable and its derivative occur in the first degree only and are not multiplied together, the differential equation is called linear differential equation The mth order linear differential equation is of the form dm_1 dx d" dy + Prm-1 (x) dx + Pm (x) y 0(x), where P,(x), P,(X) .P(x) are called the coefficients of the differential equation. NOTE:+ y2 sinx Inx is not a Linear differential equation dx MATHEMATICS FOR IIT-JEE ER. VINEET LOOMBA (IIT RooRKee)

FOR 100% SUCCESS IN JEE MAIN AND ADVANCED (IIT-JEE) Linear differential equations of first order: dy The differential equation x+ Py Q, is linear in y. where P and Q are functions of x Integrating Factor (I.F.) It is an expression which when multiplied to a differential equation converts it into an exact form. I.F for linear differential equation Pdx :. Solution of the differential equations is MATHEMATICS FOR IIT-JEE ER. VINEET LOOMBA (IIT RooRKEE)

FOR 100% SUCCESS IN JEE MAIN AND ADVANCED (IIT-JEE) dy 3x2 dx 1+X 2 sin x Example Solve dy Solution. 2 IF- P.dx- fex_dx General solution is y(IF) =|Q(IF).dx+c 2 1-cos2x y (1 +x3) (1 + x3) dx + cy(1 x3)- 2 MATHEMATICS FOR IIT-JEE ER. VINEET LOOMBA (IIT RooRKee)

FOR 100% SUCCESS IN JEE MAIN AND ADVANCED (IIT-JEE) dy Example: Solve 2x 6x62-2X Solution: The given equation can be written as dx 2x In x VX Hence, solution of the given differential equation is given by 3 2 1 2 MATHEMATICS FOR IIT-JEE ER. VINEET LOOMBA (IIT RooRKee)

FOR 100% SUCCESS IN JEE MAIN AND ADVANCED (IIT-JEE) Example: Solve|dy+ye*=e(1-x)ex x de Sol: The given equation can be written as dy (1) is a linear differnetial equation in y The general solution of equation (1) is given by (x-l) . -Ixdx + c v.ex(x-1) =X 2 yer (x-1) MATHEMATICS FOR IIT-JEE ER. VINEET LOOMBA (IIT RooRKee)

FOR 100% SUCCESS IN JEE MAIN AND ADVANCED (IIT-JEE) dy Example 2 Solution. 2 Xenx IF P.dx General solution is 2 y(En x) = (In x)2 + c MATHEMATICS FOR IIT-JEE ER. VINEET LOOMBA (IIT RooRKee)

FOR 100% SUCCESS IN JEE MAIN AND ADVANCED (IIT-JEE) dy Sol: The given equation can be written as dx 1+x 1+x (1) is a linear differential equation in y .:. The general solution of (1) is given by MATHEMATICS FOR IIT-JEE ER. VINEET LOOMBA (IIT RooRKee)