1. For each differential equations below, state whether the differential equation is separa- ble or not. If separable make sure to write it in a separable form (that is g(y) = h(x)). Clearly justify your answers and show your work. a. b. C. dy dx xex y√1+y² dy = 4x² - y² dr dy + y² = 3x²y²

Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
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Only need a b and c for Q1 please

Question 2
1. For each differential equations below, state whether the differential equation is separa-
ble or not. If separable make sure to write it in a separable form (that is g(y) dy = h(x)).
Clearly justify your answers and show your work.
dx
a.
b.
C.
d.
a.
dy
dx
b.
dy =
dx
dy
dx
dy
dx
xex
y√1+ y²
4x² - y²
2. Solve the following initial value problem:
dy
+ y² = 3x²y², y(0) = 1
dx
y(0) = 2
dy
dx
+ y² = 3x²y²
y-5
x3
y-5
=
x3,
Note: Your explanation should include all the calculus and algebra steps that are part
of solving each initial value problem. Your final answer should be written in the form
"y =" on the left, with a function of x on the right.
Transcribed Image Text:Question 2 1. For each differential equations below, state whether the differential equation is separa- ble or not. If separable make sure to write it in a separable form (that is g(y) dy = h(x)). Clearly justify your answers and show your work. dx a. b. C. d. a. dy dx b. dy = dx dy dx dy dx xex y√1+ y² 4x² - y² 2. Solve the following initial value problem: dy + y² = 3x²y², y(0) = 1 dx y(0) = 2 dy dx + y² = 3x²y² y-5 x3 y-5 = x3, Note: Your explanation should include all the calculus and algebra steps that are part of solving each initial value problem. Your final answer should be written in the form "y =" on the left, with a function of x on the right.
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