Homework Help is Here – Start Your Trial Now!
Math
Calculus
Find the general solution for the following differential equations 1. 2y" + 18y = 6tan 3x

Find the general solution for the following differential equations 1. 2y" + 18y = 6tan 3x

Calculus For The Life Sciences
Calculus For The Life Sciences
2nd Edition
ISBN:9780321964038
Author:GREENWELL, Raymond N., RITCHEY, Nathan P., Lial, Margaret L.
Publisher:GREENWELL, Raymond N., RITCHEY, Nathan P., Lial, Margaret L.
Chapter11: Differential Equations
Section11.CR: Chapter 11 Review
Problem 34CR
See similar textbooks
icon
Related questions
Question

STRICTLY HANDWRITTEN THEN BOX THE FINAL ANSWERS

Find the general solution for the following differential equations 1. 2y" + 18y = 6tan 3x 2. (D-1)² = +1
Transcribed Image Text:Find the general solution for the following differential equations 1. 2y" + 18y = 6tan 3x 2. (D-1)² = +1
Expert Solution
trending now

Trending now

This is a popular solution!

steps

Step by step

Solved in 6 steps with 5 images

SEE SOLUTIONCheck out a sample Q&A here
Blurred answer
Follow-up Questions
Read through expert solutions to related follow-up questions below.
Follow-up Question

CAN YOU RE-ANSWER #1 USING THE AUXILIARY METHOD OR SOMETHING? PLS SEE THE EXAMPLES IN THE PHOTOS.

Name: & Year No.: ger 2 11 y U m √= 2X -"ye = C₁ e² 2 -4m + 4 + 4x + 4 = (m - 2)² = 0 m = 2,2 4y + 4 = w = | 2 0 ²x 22x W W, = W = 11/2 2X fp = A ₂ ²x + B xe ²x 4x QY e x ²+1 -xe 2x 2xe ²x te" - (2 x=²*+e ²*) (e²*)-(xe²*) (²²) 2x+24x-2x64* x² +1 2x e 20² th2 xe y²+1 tet 2Y e zy x²+) 2x e²x te ²x -((e²*) (1) 2/x 2X 2X x²+1 = (E¹) (47₁) - O e A B' ур W₁ CI W I ·S. W2 W -xeyr X #S (1 u F let y = x² +1 - 1/2/3 in 1x² +11 الاول In/ x = du = 2x dx = -du-xd x -—-—- Irku) B () = 7+1 arctan () = 2 xet + 1 X x ²+1 e 2x t(arctanle) xẻ xe 2x 2 X yp=== Infr²+1/e²x + artan (x) xe² у = ус тур 2X 2X 2x Ty = G₁ e ²x + 6₁₂ xe ²x - 2/2 In / x ² + 1/ e² tartant) xe
Transcribed Image Text:Name: & Year No.: ger 2 11 y U m √= 2X -"ye = C₁ e² 2 -4m + 4 + 4x + 4 = (m - 2)² = 0 m = 2,2 4y + 4 = w = | 2 0 ²x 22x W W, = W = 11/2 2X fp = A ₂ ²x + B xe ²x 4x QY e x ²+1 -xe 2x 2xe ²x te" - (2 x=²*+e ²*) (e²*)-(xe²*) (²²) 2x+24x-2x64* x² +1 2x e 20² th2 xe y²+1 tet 2Y e zy x²+) 2x e²x te ²x -((e²*) (1) 2/x 2X 2X x²+1 = (E¹) (47₁) - O e A B' ур W₁ CI W I ·S. W2 W -xeyr X #S (1 u F let y = x² +1 - 1/2/3 in 1x² +11 الاول In/ x = du = 2x dx = -du-xd x -—-—- Irku) B () = 7+1 arctan () = 2 xet + 1 X x ²+1 e 2x t(arctanle) xẻ xe 2x 2 X yp=== Infr²+1/e²x + artan (x) xe² у = ус тур 2X 2X 2x Ty = G₁ e ²x + 6₁₂ xe ²x - 2/2 In / x ² + 1/ e² tartant) xe
_L (D) y)=P(x) _Yc = C₁ y₁ + C₂Y₂ Variation of Parameters Yp = V₁ U₁ + V₂ Y₂ _y' = U₁ y'₁ + U₁' Y₁ + Ua Ya ₁ + Uz ¹ Y ₂ tet: + _y₁ = U₁ y ₁"' + n₂ Yo' y " = U₁ y ₁ " + U ₁ Y ₁ + Uz Y₂" + la! Yo! L (D)y p(x) ay" +by' + cy = P(X) _y² + y = tan Ⓡx AE: m² + 1 = 0 ma=-1 U₂¹=vPC x -cos X | U₂ = in /vec x ttany [-viny -Wivinx + U₂' cos x = tan ex U₁' cor x + y₂' vin x = D. U₁' cor x = - U₂' viny U₁' = -U₂¹ VINY сок у -U₁ 'vin x cos x + 4₂' car @ x = tan ex corx U₁' cor x vin x + U₂'sin 2 y = 0 1 ष Ug car 2x + vin ³ x ] = [ vin x 78 car corx |u₂¹ = cor²x corx = _U₁' = U₁ _y₁ = -1₁ vin x +U₂ cov X _y"=-u₁' vinx - U₁ corx + - U₂ rin x + U ₂¹ cos x) U₁'= -vin³x -(1-corex ) viny corax covo X I vin x [uery] vindy [UIAY cory m = ± 1 Fur: fear x₁ vinx } |Y₁ = C₁ car x 1 C₂ vinx y = U₁ corx tuasiny Up = U₁ cor x + l₂ vin x y = (-vec x - car x) carx + (in /vecx + tanx) vin x) rin x 1x|- _y₁ = U₂₁ [-vin x) + U₁ CDs x tua (carx) + ug 'vinx y = recxcorx-cor@x+rin x In | rec x + ten x / -sin ³x U₁' cos x + la vin x = 0 y = -(cor+) (cos x) - cas @x-sm x + vinx (n / vecxtanx/ y = -1 -1 +0A x In reaat tany | Yp = sinx in /vec x tany - -2 vin x-viny cov? X cov oy sinx CONX tan x vecx trinx =-vecy - corx "1 _y" + y = tan@ x (-U₁' vin x - U1₁ cor x - U₂ vin x + U₂¹ carx) + (U₁corx + U₂ sin x) = tan@ y 7 car x (Coxx) xinx ] y = c₁ cv x + Coviny + vin x / n /recx+tan/₂ Y blueberry
Transcribed Image Text:_L (D) y)=P(x) _Yc = C₁ y₁ + C₂Y₂ Variation of Parameters Yp = V₁ U₁ + V₂ Y₂ _y' = U₁ y'₁ + U₁' Y₁ + Ua Ya ₁ + Uz ¹ Y ₂ tet: + _y₁ = U₁ y ₁"' + n₂ Yo' y " = U₁ y ₁ " + U ₁ Y ₁ + Uz Y₂" + la! Yo! L (D)y p(x) ay" +by' + cy = P(X) _y² + y = tan Ⓡx AE: m² + 1 = 0 ma=-1 U₂¹=vPC x -cos X | U₂ = in /vec x ttany [-viny -Wivinx + U₂' cos x = tan ex U₁' cor x + y₂' vin x = D. U₁' cor x = - U₂' viny U₁' = -U₂¹ VINY сок у -U₁ 'vin x cos x + 4₂' car @ x = tan ex corx U₁' cor x vin x + U₂'sin 2 y = 0 1 ष Ug car 2x + vin ³ x ] = [ vin x 78 car corx |u₂¹ = cor²x corx = _U₁' = U₁ _y₁ = -1₁ vin x +U₂ cov X _y"=-u₁' vinx - U₁ corx + - U₂ rin x + U ₂¹ cos x) U₁'= -vin³x -(1-corex ) viny corax covo X I vin x [uery] vindy [UIAY cory m = ± 1 Fur: fear x₁ vinx } |Y₁ = C₁ car x 1 C₂ vinx y = U₁ corx tuasiny Up = U₁ cor x + l₂ vin x y = (-vec x - car x) carx + (in /vecx + tanx) vin x) rin x 1x|- _y₁ = U₂₁ [-vin x) + U₁ CDs x tua (carx) + ug 'vinx y = recxcorx-cor@x+rin x In | rec x + ten x / -sin ³x U₁' cos x + la vin x = 0 y = -(cor+) (cos x) - cas @x-sm x + vinx (n / vecxtanx/ y = -1 -1 +0A x In reaat tany | Yp = sinx in /vec x tany - -2 vin x-viny cov? X cov oy sinx CONX tan x vecx trinx =-vecy - corx "1 _y" + y = tan@ x (-U₁' vin x - U1₁ cor x - U₂ vin x + U₂¹ carx) + (U₁corx + U₂ sin x) = tan@ y 7 car x (Coxx) xinx ] y = c₁ cv x + Coviny + vin x / n /recx+tan/₂ Y blueberry
Solution
Bartleby Expert
SEE SOLUTION
Follow-up Question

pls answer #2. STRICTLY HANDWRITTEN THEN BOX THE FINAL ANSWERS

Solution
Bartleby Expert
SEE SOLUTION
Recommended textbooks for you
Calculus For The Life Sciences
Calculus For The Life Sciences
Calculus
ISBN:
9780321964038
Author:
GREENWELL, Raymond N., RITCHEY, Nathan P., Lial, Margaret L.
Publisher:
Pearson Addison Wesley,
SEE MORE TEXTBOOKS