Lecture Notes Saturday, July 9, 2022 6:53 AM Q4: Solve the given differential equation. Find only. dx Ja'y Example 5 Sol

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Lecture Notes Saturday July 9 2022 6 53 Am Q4 Solve The Given Differential Equation Find Only Dx Ja Y Example 5 Sol 1 (35.36 KiB) Viewed 48 times

Lecture Notes Saturday, July 9, 2022 6:53 AM Q4: Solve the given differential equation. Find only. dx Ja'y Example 5 Solve the given Differential equation by variation of parameters x³y-9xy +25y = 0 For substitution x-e' or t= Inx we need to compute y, and y": y'm dy 1 1 dy dtxx dt dy 1 d x dx 1 y" 2² dy dx d'y dt d'y d'y dt Substitute in the given DE and simplify d'y dy 1 dy -9x x dy dt dt dx d (dy dx² dx dx dx/ 1 ddy 1 dy dy dt dy dt +25y-0 +25y=0 dy d y=c₁e+c₂tel Back substitute tw Inx. y-c₁e+c₂(lnx) y = c₂x² + ₂x³ (Inx) 1 (d'y dy dt 219 dy 10 +25y = 0 dt dt The result is linear DE with constant coefficients. Its auxiliary equation is m²-10m+25-0 (m-5)²-0 m₂ m₂5 repeated real roots with multiplicity k-2 case 2 The general solution of the homogeneous equation is