Solve the equation!. 0 Y'(t) = −Y(t) + sin(t) + cos(t) Y(t) = sin(t) + ce-t. Y'(t) = [Y(t) - Y(t)²] /t, Y( ▪ Y'(t) = cos²(Y(t)), Y(0) = π Y'(t) = Y(t) [Y(t)-1], Y(0)

Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
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Solve the equation! -
0 Y'(t) = -Y(t) + sin(t) + cos(t), Y(0) = 1;
Y(t) = sin(t) + ce-t.
Y'(t) = [Y(t) - Y(t)2] /t, Y(1) = 2; y(t) = t/(t+c), t> 0.
▪ Y'(t) = cos² (Y(t)), Y(0) = π/4; Y(t) = tan-¹(t + c).
Y'(t) = Y(t)[Y(t)-1],
Y(0) = 1/2; Y(t) = 1/(1+ cet).
Transcribed Image Text:Solve the equation! - 0 Y'(t) = -Y(t) + sin(t) + cos(t), Y(0) = 1; Y(t) = sin(t) + ce-t. Y'(t) = [Y(t) - Y(t)2] /t, Y(1) = 2; y(t) = t/(t+c), t> 0. ▪ Y'(t) = cos² (Y(t)), Y(0) = π/4; Y(t) = tan-¹(t + c). Y'(t) = Y(t)[Y(t)-1], Y(0) = 1/2; Y(t) = 1/(1+ cet).
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