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(1) Given the differential equation: dy y²+4y; dt Calculate and sketch the regions on the plane := R²: (a) N₁ := {(t, y) = R² : > 0}; (b) 2 = {(t, y) = R²: <0}; == (c) 3 = {(t, y) = R² = 0}; = : d 23 := (d) 4 = {(t, y) = R²: > 0}; == ΕΠ dy (e) 5 = {(t, y) = R²: <0}; 26 == (f) N6 = {(t, y) = R² ² = 0}. (g) Find the isoclines Ic := {(t, y) = R² : // = c}, for c = (h) Calculate and sketch the integral curves. = -4, -3, 0, 5, and 12.

(1) Given the differential equation: dy y²+4y; dt Calculate and sketch the regions on the plane := R²: (a) N₁ := {(t, y) = R² : > 0}; (b) 2 = {(t, y) = R²: <0}; == (c) 3 = {(t, y) = R² = 0}; = : d 23 := (d) 4 = {(t, y) = R²: > 0}; == ΕΠ dy (e) 5 = {(t, y) = R²: <0}; 26 == (f) N6 = {(t, y) = R² ² = 0}. (g) Find the isoclines Ic := {(t, y) = R² : // = c}, for c = (h) Calculate and sketch the integral curves. = -4, -3, 0, 5, and 12.

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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(1) Given the differential equation: dy y²+4y; dt Calculate and sketch the regions on the plane := R²: (a) N₁ := {(t, y) = R² : > 0}; (b) 2 = {(t, y) = R²: <0}; == (c) 3 = {(t, y) = R² = 0}; = : d 23 := (d) 4 = {(t, y) = R²: > 0}; == ΕΠ dy (e) 5 = {(t, y) = R²: <0}; 26 == (f) N6 = {(t, y) = R² ² = 0}. (g) Find the isoclines Ic := {(t, y) = R² : // = c}, for c = (h) Calculate and sketch the integral curves. = -4, -3, 0, 5, and 12.
Transcribed Image Text:(1) Given the differential equation: dy y²+4y; dt Calculate and sketch the regions on the plane := R²: (a) N₁ := {(t, y) = R² : > 0}; (b) 2 = {(t, y) = R²: <0}; == (c) 3 = {(t, y) = R² = 0}; = : d 23 := (d) 4 = {(t, y) = R²: > 0}; == ΕΠ dy (e) 5 = {(t, y) = R²: <0}; 26 == (f) N6 = {(t, y) = R² ² = 0}. (g) Find the isoclines Ic := {(t, y) = R² : // = c}, for c = (h) Calculate and sketch the integral curves. = -4, -3, 0, 5, and 12.
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