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4. Solve the following differential equations: (a) y' - 5y = -5ty³ (b) xy + 5y = 2x²y¹, y(1) = 3 dx

4. Solve the following differential equations: (a) y' - 5y = -5ty³ (b) xy + 5y = 2x²y¹, y(1) = 3 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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4. Solve the following differential equations: (a) y' - 5y = -5ty³ (b) xy + 5y = 2x²y¹, y(1) = 3 dx
Transcribed Image Text:4. Solve the following differential equations: (a) y' - 5y = -5ty³ (b) xy + 5y = 2x²y¹, y(1) = 3 dx
Expert Solution
Step 1: Write the given differential equations

Given space that space the space differential space equations space left parenthesis straight a right parenthesis space y apostrophe minus 5 y equals negative 5 t y cubed open parentheses b close parentheses space x space fraction numerator d y over denominator d x end fraction plus 5 y equals 2 x squared y to the power of 4 space space comma space space y open parentheses 1 close parentheses equals 3

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