PLEASEEEE HELPP MEEE WITHHH NUMBERSSS 9 AND 10 PLEASEEE HELPPP MEEEEE!!!!!!!!
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Answer:
Linear second-order differential equation F(x, y, y′, y″) = 0
y¹¹( -3 x⁴ )+ y¹12 x³ - 12 x² y= 0
Step-by-step explanation:
<u><em>Step(i):-</em></u>
Given differential equation
y = c₁x + c₂x⁴ ...(i)
Differentiating equation (i) with respective to 'x', we get
y¹ = c₁(1) + c₂ ( 4 x³ ) ...(ii)
Differentiating equation (ii) with respective to 'x', we get
y¹¹ = c₂ ( 12 x² )
...(a)
<u><em>Step(ii)</em></u>:-
Substitute (a) in equation (ii)
...(b)
<u><em>Step(iii):</em></u>-
12 x² y = (y¹12 x³ - 4 x⁴ y¹¹) + x⁴ y¹¹
x⁴ y¹¹ - 4 x⁴ y¹¹ + y¹12 x³ - 12 x² y= 0
y¹¹( -3 x⁴ )+ y¹12 x³ - 12 x² y= 0