Determine that each equation is a solution of the given differential equation. y = A sin 5x + B cos 5x; d²y dx² +25y = 0 x = 5 cost - 7 sint; x" + x = 0 y=e-2x; y'"-3y' + 2y = 0 y = 2e x + xe-*; y" + 2y' + y = 0 1. 2. 3. 4. 5. Y = C₁e* + C₂xe* + C3e¯x + 2x²ex, d³y_d²y_ dy +y-8e* = 0 dx³ dx² dx -
Determine that each equation is a solution of the given differential equation. y = A sin 5x + B cos 5x; d²y dx² +25y = 0 x = 5 cost - 7 sint; x" + x = 0 y=e-2x; y'"-3y' + 2y = 0 y = 2e x + xe-*; y" + 2y' + y = 0 1. 2. 3. 4. 5. Y = C₁e* + C₂xe* + C3e¯x + 2x²ex, d³y_d²y_ dy +y-8e* = 0 dx³ dx² dx -
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.CR: Chapter 11 Review
Problem 33CR
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Determine that each equation is a solution of the given differential equation.
Transcribed Image Text:Determine that each equation is a solution of the given differential equation.
d²y
y = A sin 5x + B cos 5x;
+25y = 0
dx²
x = 5 cost - 7 sint; x" + x = 0
1.
2.
3.
4.
5.
y=e-²x; y"" - 3y' + 2y = 0
y = 2e-x + xe-x; y" + 2y' + y = 0
y = C₁e* + C₂xe* + c3e-* + 2x²e*;
d³y
dx³
-
d²y dy
dx² dx
+y-8e* = 0
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