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1. Find a particular solution in the given equation which satisfies the indicated conditions. (1+x2)dy = (1+xy)dx . @ x=1, y=0

1. Find a particular solution in the given equation which satisfies the indicated conditions. (1+x2)dy = (1+xy)dx . @ x=1, y=0

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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This is a Differential Equation exercise. Please answer it clean with complete solution. Thank you and keep safe!

1. Find a particular solution in the given equation which satisfies the indicated conditions. (1+x?)dy = (1+xy)dx .@ x=1, y=0 2. Show that the substitution z=y(l-n) will reduce the Bernoulli Equation y' + f(x)y = Q(x)y" to a linear 1st order equation. 3. Solve the given equation by two methods 2ydx + (3y-2x)dy = 0 4. Solve the given equation and discuss the family of solution dy/dx = (x-y)/(x+3y) 5. Find the solution of the ff equations a. y' = 2 (y+1). %3D (x+1) b. y' + (y')2 +1= 0
Transcribed Image Text:1. Find a particular solution in the given equation which satisfies the indicated conditions. (1+x?)dy = (1+xy)dx .@ x=1, y=0 2. Show that the substitution z=y(l-n) will reduce the Bernoulli Equation y' + f(x)y = Q(x)y" to a linear 1st order equation. 3. Solve the given equation by two methods 2ydx + (3y-2x)dy = 0 4. Solve the given equation and discuss the family of solution dy/dx = (x-y)/(x+3y) 5. Find the solution of the ff equations a. y' = 2 (y+1). %3D (x+1) b. y' + (y')2 +1= 0
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