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Verify that the indicated family of functions is a solution of the given differential equation. Assume an appropriate interval I of definition for each solution. d²y - 85 dy dx² dx When y = c₁e4x + c₂xe¹x, dy dx d²y dx = + 16y=0; y = c₂e4x + ₂xe4x Thus, in terms of x, d²y dx² -8dy + 16y= dx + 16(CqeX + Cyxex)

Verify that the indicated family of functions is a solution of the given differential equation. Assume an appropriate interval I of definition for each solution. d²y - 85 dy dx² dx When y = c₁e4x + c₂xe¹x, dy dx d²y dx = + 16y=0; y = c₂e4x + ₂xe4x Thus, in terms of x, d²y dx² -8dy + 16y= dx + 16(CqeX + Cyxex)

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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Verify that the indicated family of functions is a solution of the given differential equation. Assume an appropriate interval I of definition for each solution. d²y dy 8 + 16y = 0; y = c₁e¹x + ₂x²¹x dx2 dx When y = c₁e4x + c₂xe¹x, dy dx d²y dx² || - || Thus, in terms of x, d²y dx² dy 8 + 16y= dx 11 4x + 16(c1e*X + c_xe*x)
Transcribed Image Text:Verify that the indicated family of functions is a solution of the given differential equation. Assume an appropriate interval I of definition for each solution. d²y dy 8 + 16y = 0; y = c₁e¹x + ₂x²¹x dx2 dx When y = c₁e4x + c₂xe¹x, dy dx d²y dx² || - || Thus, in terms of x, d²y dx² dy 8 + 16y= dx 11 4x + 16(c1e*X + c_xe*x)
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