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N(x, y) = xy Step 2 The equation M(x, y) dx + N(x, y) dy = 0 is said to be homogeneous if there is a real number a such that M(tx, ty) = M(x, y) and N(tx, ty) = taN(x, y). M(tx, ty) = -(ty)³ + (tx)³ -) (-x³ + x³) M(x, y) = N(tx, ty) = (tx) (ty)² )(xy2) xy² N(X, Y) Therefore, the equation is homogeneous where a =

N(x, y) = xy Step 2 The equation M(x, y) dx + N(x, y) dy = 0 is said to be homogeneous if there is a real number a such that M(tx, ty) = M(x, y) and N(tx, ty) = taN(x, y). M(tx, ty) = -(ty)³ + (tx)³ -) (-x³ + x³) M(x, y) = N(tx, ty) = (tx) (ty)² )(xy2) xy² N(X, Y) Therefore, the equation is homogeneous where a =

Advanced Engineering Mathematics
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 step 2 ty.

Step 1 We are given a differential equation and will rewrite it in the form M(x, y) dx + N(x, y) dy = 0. Find the functions M and N. M(x, y) = N(x, y) = xy² dy - (³x³) dx = 0 xy2 dy + (-y³ + x³) dx = 0 xy² xy² dx = y³ – x³ xy2 dy = (y3x³) dx N(tx, ty) = (tx) (ty)² Step 2 The equation M(x, y) dx + N(x, y) dy = 0 is said to be homogeneous if there is a real number a such that M(tx, ty) = M(x, y) and N(tx, ty) = N(x, y). M(tx, ty) = -(ty)³ + (tx)³ )c-v3 + M(x, y) 73 )(xy²) ry² + x³) N(x, y) Therefore, the equation is homogeneous where a =
Transcribed Image Text:Step 1 We are given a differential equation and will rewrite it in the form M(x, y) dx + N(x, y) dy = 0. Find the functions M and N. M(x, y) = N(x, y) = xy² dy - (³x³) dx = 0 xy2 dy + (-y³ + x³) dx = 0 xy² xy² dx = y³ – x³ xy2 dy = (y3x³) dx N(tx, ty) = (tx) (ty)² Step 2 The equation M(x, y) dx + N(x, y) dy = 0 is said to be homogeneous if there is a real number a such that M(tx, ty) = M(x, y) and N(tx, ty) = N(x, y). M(tx, ty) = -(ty)³ + (tx)³ )c-v3 + M(x, y) 73 )(xy²) ry² + x³) N(x, y) Therefore, the equation is homogeneous where a =
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