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Solve the differential equation by variation of parameters. y" + 3y + 2y = 4 + ex Step 1 We are given a nonhomogeneous second-order differential equation. Similar to the method of solving by undetermined coefficients, we first find the complementary function y for the associated homogeneous equation. This time, the particular solution y, is based on Wronskian determinants and the general solution is y = y + Yp' First, we must find the roots of the auxiliary equation for y" + 3y + 2y = 0. m² +3m + 2 = 0 Solving for m, the roots of the auxiliary equation are as follows. smaller value m₂ = larger value m₂ =

Solve the differential equation by variation of parameters. y" + 3y + 2y = 4 + ex Step 1 We are given a nonhomogeneous second-order differential equation. Similar to the method of solving by undetermined coefficients, we first find the complementary function y for the associated homogeneous equation. This time, the particular solution y, is based on Wronskian determinants and the general solution is y = y + Yp' First, we must find the roots of the auxiliary equation for y" + 3y + 2y = 0. m² +3m + 2 = 0 Solving for m, the roots of the auxiliary equation are as follows. smaller value m₂ = larger value m₂ =

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 differential equation by variation of parameters. 1 4 + e* y" + 3y' + 2y = Step 1 is We are given a nonhomogeneous second-order differential equation. Similar to the method of solving by undetermined coefficients, we first find the complementary function y for the associated homogeneous equation. This time, the particular solution yp based on Wronskian determinants and the general solution is y = y + Yp' First, we must find the roots of the auxiliary equation for y" + 3y' + 2y = 0. m² +3m + 2 = 0 Solving for m, the roots of the auxiliary equation are as follows. smaller value larger value m₁ = m₂ =
Transcribed Image Text:Solve the differential equation by variation of parameters. 1 4 + e* y" + 3y' + 2y = Step 1 is We are given a nonhomogeneous second-order differential equation. Similar to the method of solving by undetermined coefficients, we first find the complementary function y for the associated homogeneous equation. This time, the particular solution yp based on Wronskian determinants and the general solution is y = y + Yp' First, we must find the roots of the auxiliary equation for y" + 3y' + 2y = 0. m² +3m + 2 = 0 Solving for m, the roots of the auxiliary equation are as follows. smaller value larger value m₁ = m₂ =
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