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on the interval (0. r³y" + 6x³y + 4xy' - 4y = 0

on the interval (0. r³y" + 6x³y + 4xy' - 4y = 0

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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Solve the Cauchy-Euler differential equation on the interval (0,00). Question Use undetermined coefficients to solve the differential equation y"-y=e* -x + 16. x³y" + 6x²y" + 4xy' - 4y = 0 Question Use variation of parameters to solve the differential equation 2²y" + 10xy' +8y=x². Question 65 (a) (i) use the definition of C{-} to determine {te"). (ii) Evaluate L-¹{4}. (b) Solve the initial value problem by Laplace transforms. y" - 3y + 2y = 0, y(0) = -3, y/(0) = 5 Page 3 of 3 Question 7 (a) List all the singular points of x² (1-x)³y" + (1+2x)y = 0. ди ди Эх ду 11 (b) Use the method of separation of variables to determine the function u(x, y) which satisfies the following partial differential equation together with the given condition: = 0; u(x,0)=4e-3. THES] Y Pre
Transcribed Image Text:Solve the Cauchy-Euler differential equation on the interval (0,00). Question Use undetermined coefficients to solve the differential equation y"-y=e* -x + 16. x³y" + 6x²y" + 4xy' - 4y = 0 Question Use variation of parameters to solve the differential equation 2²y" + 10xy' +8y=x². Question 65 (a) (i) use the definition of C{-} to determine {te"). (ii) Evaluate L-¹{4}. (b) Solve the initial value problem by Laplace transforms. y" - 3y + 2y = 0, y(0) = -3, y/(0) = 5 Page 3 of 3 Question 7 (a) List all the singular points of x² (1-x)³y" + (1+2x)y = 0. ди ди Эх ду 11 (b) Use the method of separation of variables to determine the function u(x, y) which satisfies the following partial differential equation together with the given condition: = 0; u(x,0)=4e-3. THES] Y Pre
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