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Examples on Linear Differential Equation
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This lesson takes up more problems on linear differential equation form

Vineet Loomba is teaching live on Unacademy Plus

U
M
good job refer by mandeep
Sy
sir linear differential equations for 2nd order plzzz????
Sir at 10:34 to solve the integral on rhs I tried to use the property e^x(f(x)+f'(x)) and my general solution is little different from yours . Please guide sir.
Jm
sir plz give solution for question no 4 lesson 11 practice yourself
sir aapne bola tha aur lesson add honge. equations reduceable to linear form. plzzz sir add kr dijiye. Mains ke liye important hai.
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) 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)

5. 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)

6. 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)

7. 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)

8. 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)

9. 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)

10. 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)