## 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) 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)

FOR 100% SUCCESS IN JEE MAIN AND ADVANCED (IIT-JEE) Solve the differential equation t(1 + t2) dx = (x + xts_ t?) dt and it is given that x--n4 at t = 1 t(1 + t2) dx [x (1 + t2)-t ] dt Example : Solution. dt 1+t2 which is linear in-: Here, P = -+, dt IF= e e-int- General solution is- x tan-1 t c x =-t tan-1 t MATHEMATICS FOR IIT-JEE ER. VINEET LOOMBA (IIT RooRKee)

FOR 100% SUCCESS IN JEE MAIN AND ADVANCED (11T-JEE) If the differential equation has the following form dx where P, and Q, are functions ofy The I.F. now is ely . MATHEMATICS FOR IIT-JEE ER. VINEET LOOMBA (IIT RooRKEE)

FOR 100% SUCCESS N JEE MAIN AND ADVANCED (IIT-JEE) Example: Solve (**y- i(-1 Sol: The given equation is not a linear equation in y. It can be written as-= x + y + 1 which is LD.E. in x. dr dr dy dhr dy The general solution of equation ( 1 ) is This is the required solution. MATHEMATICS FOR IIT-JEE ER. VINEET LOOMBA (IIT RooRKEE)

FOR 100% SUCCESS IN JEE MAIN AND ADVANCED (IIT-JEE) Practice Yourself: 1 Ans. 2xe-tanny +c dy dy -ytan x 2sinx dx 2 Ans. y = secx(-sin x + c ) dy 4 sin X 3y - cos x. 2 2 MATHEMATICS FOR IIT-JEE ER. VINEET LOOMBA (IIT RooRKee)