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### Calculus - Differential Equations Problem Set II - D operator, Linear Differential Equations, Auxiliary equations, Finding general solution ( CF + PI )

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## Calculus - Differential Equations Problem Set II- Outline of Contents:

### Target Audience: High School Students, College Freshmen and Sophomores, students preparing for the International Baccalaureate (IB), AP Calculus AB, AP Calculus BC, A Level, Singapore/GCE A-Level; Class 11/12 students in India preparing for ISC/CBSE and Entrance Examinations like the IIT-JEE/AIEEE Anyone else who needs this Tutorial as a reference!

In this tutorial, we will take a look at some examples and solved problems - Solving linear differential equations, the D operator, auxiliary equations. Finding the general solution ( CF + PI )
Here's a quick outline of the kind of equations we will learn how to solve.

### We will solve the following linear diﬀerential equations, finding auxillary equations and general solutions.

(D3 + 6D2 + 11D + 6)y = 0
(D4 − 4D3 + 8D2 − 8D + 4)y = 0
(D4 + 2D3 + 3D2 + 2D + 1)y = 0
(D4 − D3 − 9D2 − 11D − 4)y = 0
(D2 + a2 )y = cot ax
(i)(D2 − 3D + 2)y = e3x
(D2 − 2D + 1)y = 2e 2

### In Case you'd like to take a look at some of our other tutorials related to Single Variable Calculus :

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Functions, Limits and Continuity - Solved Problem Set II - Conditions for Continuity, More Limits, Approximations for ln (1+x) and sin x for infinitesimal values of x   - More advanced cases of evaluating limits, conditions for continuity of functions, common approximations used while evaluating limits for ln ( 1 + x ), sin (x); continuity related problems for more advanced functions than the ones in the first group of problems (in the last tutorial). Functions, Limits and Continuity - Solved Problem Set III - Continuity and Intermediate Value Theorems - Problems related to Continuity, intermediate value theorem. 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Differential Calculus - Solved Problem Set II - Derivability and continuity of functins - Change of Indepndent Variables - Finding N-th Derivatives - Examples and solved problems - related to derivability and continuity of functions; changing the independent variable in a differential equation; finding the N-th derivative of functions Differential Calculus - Solved Problems Set III- Maximia, Minima, Extreme Values,  Rolle's Theorem - Examples and solved problems - related to increasing and decreasing functions; maxima, minima and extreme values; Rolle's Theorem Differential Calculus - Solved Problems Set IV - Points of Inflexion, Radius of Curvature, Curve Sketching -  Examples and solved problems - Slope of tangents to a curve, points of inflexion, convexity and concavity of curves, radius of curvature and asymptotes of curves, sketching curves Differential Calculus - Solved Problems Set V - Curve Sketching, Parametric Curves - More examples of investigating and sketching curves, parametric representation of curves Introducing Integral Calculus - Definite and Indefinite Integrals - using Substitution , Integration By Parts, ILATE rule  - Theory and definitions. 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