Explanation of Solution Given information: The equation is z = xy and Calculation: Consider the equation. √ 2x³ + 2y³ = 3t² 3x² + 3y² 6t Differentiate above equation. 6x2 dx + 6y²5 dt z = xy² z = xy dx dt = 6x dx + 6y. dt = t-y x(x-y) (y² - xy) dy dt The solution of above simultaneous equation is, (x² − xy) dx = t - y dt dy dt = t-x y(y-x) dt - = t-x = 6 6t 2x³ + 2y³ = 31² 3x² + 3y² 6t =

Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
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Please explain steps after part that says: solving simultaneously" 

Explanation of Solution
Given information: The equation is z = xy and
Calculation:
Consider the equation.
√ 2x³ + 2y³
| 3x² + 3y²
z = xy
z = xy<
Differentiate above equation.
2 dx
6x²x+6y² = 6t
2 dy
dt
dt
dx
dt
(y² - xy)
dy
dt
=
-
=
dy
6x dx + 6y
dt
dt
=
The solution of above simultaneous equation is,
(x² - xy) dx = t-y
t-y
x(x-y)
dy
dt
t-x
y(y-x)
31²
6t
= t-x
= 6
√ 2x³ + 2y³ = 3t²
3x² + 3y² = 6t
Transcribed Image Text:Explanation of Solution Given information: The equation is z = xy and Calculation: Consider the equation. √ 2x³ + 2y³ | 3x² + 3y² z = xy z = xy< Differentiate above equation. 2 dx 6x²x+6y² = 6t 2 dy dt dt dx dt (y² - xy) dy dt = - = dy 6x dx + 6y dt dt = The solution of above simultaneous equation is, (x² - xy) dx = t-y t-y x(x-y) dy dt t-x y(y-x) 31² 6t = t-x = 6 √ 2x³ + 2y³ = 3t² 3x² + 3y² = 6t
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