c) d'y 1 dy + dx² x dx = 0, x > 0, y₁ = ln x
Calculus For The Life Sciences
2nd Edition
ISBN:9780321964038
Author:GREENWELL, Raymond N., RITCHEY, Nathan P., Lial, Margaret L.
Publisher:GREENWELL, Raymond N., RITCHEY, Nathan P., Lial, Margaret L.
Chapter11: Differential Equations
Section11.1: Solutions Of Elementary And Separable Differential Equations
Problem 9E: Find the general solution for each differential equation. Verify that each solution satisfies the...
Related questions
Question
Question 1C
![1. Show that given function is a solution of the differential equation. Then solve the
equation by finding a general solution.
b)
c)
d)
d'y 1 dy
dx²
x dx
x²
d'y
dx
d'y
dx²
+
2x
1 dy
x dx
e) (1-x²).
- 4x²y = 0, -∞ < x < ₁ = ²
d'y
dx²
dy
·+ (x² + 2)y = 0, x > 0, y₁ = x sin x
dx
-= 0, x > 0, y₁ = ln x
d²y_1 dy + 4x²y = 0, x > 0, y₁ = sin(x²)
dx²
x dx
2x.
dy + 2y = 0, -1 < x < 1, y₁ = x
dx
30](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F4d410cd6-8fc6-4d13-8ff0-7a43ba3056bc%2F141b6d4a-482d-4922-a297-304bd4b7ba18%2Fv1zujcp_processed.jpeg&w=3840&q=75)
Transcribed Image Text:1. Show that given function is a solution of the differential equation. Then solve the
equation by finding a general solution.
b)
c)
d)
d'y 1 dy
dx²
x dx
x²
d'y
dx
d'y
dx²
+
2x
1 dy
x dx
e) (1-x²).
- 4x²y = 0, -∞ < x < ₁ = ²
d'y
dx²
dy
·+ (x² + 2)y = 0, x > 0, y₁ = x sin x
dx
-= 0, x > 0, y₁ = ln x
d²y_1 dy + 4x²y = 0, x > 0, y₁ = sin(x²)
dx²
x dx
2x.
dy + 2y = 0, -1 < x < 1, y₁ = x
dx
30
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