no need to solve. just write everything digitally. thank you. i will upvote (2) = -√²)y = x³²c* ; x = 1, y=0dxP(x) = = = = Q(x) = x ² exStep 1: Integrate P(x)SPCx) dx = S÷dx = -2 Inlxl = lr|x²| = In x^²Step 2: Substitute it into the integrating factorSP(x) dxeInx-2e#Integrate:Yx² = ex+cXYø=SØ QCxdx + cY x ² = S x²(x^² ex) dx + CStep 3: Use the formula in solving the 1st ordered LiE.Use:Ø= espax) dx-2= X+C-Integrating factor= eX2y = x² e² + (x³²Step 4: Substitute the given value0 =(1) ² e ²0 +C (1) ²(1)(=-eBefore final answerdydxCancel termx= 1, y =oSubstitute -e to c2y=x²e² - ex²Standard form:+ P(x) y = Q(x)

Given differential equation dydx-2x y=x2 ex ; x=1 y=0

Answered: 2.) dy 1) = x - (²2²) y = x ² ex ; x =…

Math

Calculus

2.) dy 1) = x - (²2²) y = x ² ex ; x = 1, y = 0 dx P(x) = = = = Q(x) = x² ex X Standard form: dy dx + P(x) y = Q(x)

Calculus: Early Transcendentals

8th Edition

ISBN:9781285741550

Author:James Stewart

Publisher:James Stewart

Chapter1: Functions And Models

Section: Chapter Questions

Problem 1RCC: (a) What is a function? What are its domain and range? (b) What is the graph of a function? (c) How...

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no need to solve. just write everything digitally. thank you. i will upvote

(2) = -√²)y = x³²c* ; x = 1, y=0
dx
P(x) = = = = Q(x) = x ² ex
Step 1: Integrate P(x)
SPCx) dx = S÷dx = -2 Inlxl = lr|x²| = In x^²
Step 2: Substitute it into the integrating factor
SP(x) dx
e
Inx-2
e
#
Integrate:
Yx² = ex+c
X
Yø=SØ QCxdx + c
Y x ² = S x²(x^² ex) dx + C
Step 3: Use the formula in solving the 1st ordered LiE.
Use:
Ø= espax) dx
-2
= X
+C
-Integrating factor
= e
X
2
y = x² e² + (x³²
Step 4: Substitute the given value
0 =(1) ² e ²0 +C (1) ²
(1)
(=-e
Before final answer
dy
dx
Cancel term
x= 1, y =o
Substitute -e to c
2
y=x²e² - ex²
Standard form:
+ P(x) y = Q(x)

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