Cauchy Euler Equations and Variation of Parameters || Differential Equations

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x^2y''-3xy'+3y=2x^4e^x

This is a good problem involving a Cauchy - Euler equation where we'll use the method of variation of parameters to find a particular solution. Be careful: there's a common error that many students make! We take our time and point out the error. You might want to review the method of variation of parameters before trying this problem; link below. More problems are linked below.

Reference Videos:
▶️Use Variation of Parameters to Solve y'''+ y'= tanx

▶️Variation of Parameters || Nonhomogeneous Second Order Differential Equations

▶️Integrals of powers of tan using Integral Reduction

▶️Annihilator Operators || Differential Operator || Differential Equation

▶️Method of Undetermined Coefficients | Superposition Approach | 20 Examples

▶️Method of Undetermined Coefficients Superposition Approach || Differential Equations

▶️Linear Higher Order Differential Equation | Distinct Roots | Repeated Roots | Complex Roots

▶️Homogeneous Differential Equation With Constant Coefficients | Higher Order | Concept | Examples

▶️Homogeneous Differential Equation With Constant Coefficients | Conjugate Complex Roots

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Example will help Engineering and Basic Science students to understand the following topic of Mathematics:
1. How to use the Variation of Parameters Method to Solve a Cauchy Euler Equation
2. Example Of Variation of Parameters Method to Solve a Cauchy Euler Equation
3. Concept Of particular solution using method of undetermined coefficients using Variation of Parameters
4. This is helpful For CSIR NET, IIT-JAM, GATE Exams.
5. This is Part Of the Differential Equation.

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  1. Sabahat Qadeer
  2. cauchy euler equation
  3. cauchy euler differential equation
  4. cauchy euler
  5. differential equations
  6. euler cauchy equations
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Is it necessary to solve yp by variation of parameter and not by other methods studied previously

Zarnab-dhillon