how that the given equation is not exact but becomes exact when multiplied by the given integrating factor. Then solve the equation. x²y3 + x(3+ y²y = 0, μ(x, y) = Here, M(x, y) = x²y³ and N(x, y) = x(3+²) x dx + 3 xy 1 y=h(y)=N=0 X ) dy x ✓ Therefore, My = 3x²2 0. Now we see that for this equation M x and N= Therefore, h(y) = 2 ✓ and N, - (3+2) ✓ Therefore, My We see that the equation is not exact. Now, multiplying the equation by u(x, y)=, the equation becomes 0 ✓ =N₂. Integrating M with respect to x, we see that , and we conclude that the solution of the equation is given implicitly by and y= 0. +h(y). Further,
how that the given equation is not exact but becomes exact when multiplied by the given integrating factor. Then solve the equation. x²y3 + x(3+ y²y = 0, μ(x, y) = Here, M(x, y) = x²y³ and N(x, y) = x(3+²) x dx + 3 xy 1 y=h(y)=N=0 X ) dy x ✓ Therefore, My = 3x²2 0. Now we see that for this equation M x and N= Therefore, h(y) = 2 ✓ and N, - (3+2) ✓ Therefore, My We see that the equation is not exact. Now, multiplying the equation by u(x, y)=, the equation becomes 0 ✓ =N₂. Integrating M with respect to x, we see that , and we conclude that the solution of the equation is given implicitly by and y= 0. +h(y). Further,
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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Please answer the wrong ty.
Transcribed Image Text:Show that the given equation is not exact but becomes exact when multiplied by the given integrating factor. Then solve the equation.
x²y³ + x(3 + y2)y' = 0, u(x, y) =
+43
x(3+1²)
Here, M(x, y) = x²y³ and N(x, y) =
x dx +
3
1
xy
. Therefore, My = 3x²1²
) dy = = 0. Now we see that for this equation M = x and N =
X
y = h'(y) = N = 0
X
. Therefore, h(y) =
2
X
and N =
+
y
(3+1²)
. Therefore, My
. We see that the equation is not exact. Now, multiplying the equation by u(x, y) = the equation becomes
=
0
= N. Integrating M with respect to x, we see that =
, and we conclude that the solution of the equation is given implicitly by
X
and y = 0.
~~
+ h(y). Further,
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