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1. You are given the nonhomogeneous equation y'+2xy = x (a) Determine an integrating factor for the equation (b) Determine the general solution of the equation. 2. Show that the differential equation cos a + In y +7+ + ey - y? ) y' = 0 is exact then solve it. 3. Show that y' (x2 + 2) = 5xy + 5x is separable then solve it. %3D 4. Solve the Bernoulli equation 2ryy'+y? = 2x2.

1. You are given the nonhomogeneous equation y'+2xy = x (a) Determine an integrating factor for the equation (b) Determine the general solution of the equation. 2. Show that the differential equation cos a + In y +7+ + ey - y? ) y' = 0 is exact then solve it. 3. Show that y' (x2 + 2) = 5xy + 5x is separable then solve it. %3D 4. Solve the Bernoulli equation 2ryy'+y? = 2x2.

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 check the attached image and answer the math questions. I really need help.

1. You are given the nonhomogeneous equation \( y' + 2xy = x \) - (a) Determine an integrating factor for the equation - (b) Determine the general solution of the equation. 2. Show that the differential equation \( \cos x + \ln y + 7 + \left( \frac{x}{y} + e^y - y^2 \right) y' = 0 \) is exact then solve it. 3. Show that \( y'(x^2 + 2) = 5xy + 5x \) is separable, then solve it. 4. Solve the Bernoulli equation \( 2xyy' + y^2 = 2x^2 \).
Transcribed Image Text:1. You are given the nonhomogeneous equation \( y' + 2xy = x \) - (a) Determine an integrating factor for the equation - (b) Determine the general solution of the equation. 2. Show that the differential equation \( \cos x + \ln y + 7 + \left( \frac{x}{y} + e^y - y^2 \right) y' = 0 \) is exact then solve it. 3. Show that \( y'(x^2 + 2) = 5xy + 5x \) is separable, then solve it. 4. Solve the Bernoulli equation \( 2xyy' + y^2 = 2x^2 \).
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