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22 Consider the linear differential equation Select one alternative: ○ (x³y)' = x² ○ (x³y)' = x³ ○ (x³y)' = x¹ (x²y)' = x¹ 3 + y = x. Which of the following formulas holds? dx

22 Consider the linear differential equation Select one alternative: ○ (x³y)' = x² ○ (x³y)' = x³ ○ (x³y)' = x¹ (x²y)' = x¹ 3 + y = x. Which of the following formulas holds? dx

Advanced Engineering Mathematics
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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22 Consider the linear differential equation Select one alternative: ○ (x³y)' = x² ○ (x³y)' = x³ ○ (x³y)' = x4 ○ (x²y)' = x¹ dy dx + 3 -y = x. Which of the following formulas holds? X
Transcribed Image Text:22 Consider the linear differential equation Select one alternative: ○ (x³y)' = x² ○ (x³y)' = x³ ○ (x³y)' = x4 ○ (x²y)' = x¹ dy dx + 3 -y = x. Which of the following formulas holds? X
Expert Solution
Step 1

The given linear differential equation is ,

              dydx+3xy = x

(.)  Solution of a first order linear differential equation of the form   dydx+P(x)y = Q(x)  is            given by ,

      y(I.F.) =∫ Q(x) (I.F.) dx + c  ;     c  is an arbitrary constant 

     where  I.F. is an integrating factor and given by ,

       I.F.   =   e∫ P(x) dx

now we solve the given linear differential equation .

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