x×y′′−y=x^3


Question and Answers Forum

All Questions Topic List
Differential Equation Questions
Previous in All Question Next in All Question
Previous in Differential Equation Next in Differential Equation
Question Number 143776 by akmalovna05 last updated on 18/Jun/21

$x \times y^{″} - y = x^{3}$
	Answered by Olaf_Thorendsen last updated on 18/Jun/21
	$xy′′−y = x^3 (1) Particular solution : y = ax^3 +bx^2 +cx+d y′ = 3ax^2 +2bx+c y′′ = 6ax+2b (1) : 6ax^2 +2bx−ax^3 −bx^2 −cx−d = x^3 { ((−a = 1)),((6a−b = 0)),((2b−c = 0)),((−d = 0)) :} a = −1, b = −6, c = −12, d = 0 y = −x^3 −6x^2 −12x Homogen solution : xy′′−y = 0 → see Bessel equation$
	${x y}^{″} - y = x^{3} (1)$ $Particular solution :$ $y = {a x}^{3} + {b x}^{2} + c x + d$ $y^{'} = 3 {a x}^{2} + 2 b x + c$ $y^{″} = 6 a x + 2 b$ $(1) : 6 {a x}^{2} + 2 b x - {a x}^{3} - {b x}^{2} - c x - d = x^{3}$ ${\begin{cases} - a = 1 \\ 6 a - b = 0 \\ 2 b - c = 0 \\ - d = 0 \end{cases}$ $a = - 1, b = - 6, c = - 12, d = 0$ $y = - x^{3} - 6 x^{2} - 12 x$ $Homogen solution :$ ${x y}^{″} - y = 0$ $\to see Bessel equation$
	Commented by SANOGO last updated on 30/Aug/21

Terms of Service
Privacy Policy
Contact: info@tinkutara.com

Question and Answers Forum