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a Separable Solve the initial value problem (2 + 1) - 2rco"(9) with y(0)- Find an explicit solution. ANSWER: y(2) = arctan (1 + In (z² + 1)) 4. Separable Solve the Initial value problem y- 3rv+ 1 see(y) with y(0) - 0. Fiad an explicit

a Separable Solve the initial value problem (2 + 1) - 2rco"(9) with y(0)- Find an explicit solution. ANSWER: y(2) = arctan (1 + In (z² + 1)) 4. Separable Solve the Initial value problem y- 3rv+ 1 see(y) with y(0) - 0. Fiad an explicit

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 IVP (r - 4)/ +y - with y(3) - 1. On what interval does the fundamental existence theory for first order initial value problems guarantee there is a unique solutjon. ANSWER: 2<I<7 3. Separable Solve the initial value problem (r² + 1)s/ = 2r cos"(y) with y(0) = Find an explicit solution ANSWER: y(z) - arctan (1 + In (+1)) 4. Separable Solve the initial value problem y = 3rV+1sec(y) with y(0) = 0. Find an explicit solution. - sin" ((1+a/a-1) ANSWER: 5. Solve the Eirst Order Lincar IVP ry +y = 3r, y(1) = 2. Find an explicit solution. ANSWER 6. Solve the Exacet equation (sin(y) – y sin(z)) dr + (1 +zcos(y) + cos(x)) dy = 0. ANSWER: z sin(y) +y cos(r) +y-C 7. Find an integrating factor and show that it is one (do not solve) 2r tan(y) dz + see*(y) dy = 0. ANSWER: µ = e*, → M = 2re" tan(y). N =* see°(y), M, = 2re" see"(y) - N, 8. Find an implicit general solution of the Homogeneous equation y= ANSWER: ry + In(a)- C 9. Use the substitution - (z-y) to solve y- (z- 9)² + 1. ANSWER: (z-v) 10. Solve the Bernoulli equation -y- ANSWER: Filters Add a caption. > My group
Transcribed Image Text:1. Given the IVP (r - 4)/ +y - with y(3) - 1. On what interval does the fundamental existence theory for first order initial value problems guarantee there is a unique solutjon. ANSWER: 2<I<7 3. Separable Solve the initial value problem (r² + 1)s/ = 2r cos"(y) with y(0) = Find an explicit solution ANSWER: y(z) - arctan (1 + In (+1)) 4. Separable Solve the initial value problem y = 3rV+1sec(y) with y(0) = 0. Find an explicit solution. - sin" ((1+a/a-1) ANSWER: 5. Solve the Eirst Order Lincar IVP ry +y = 3r, y(1) = 2. Find an explicit solution. ANSWER 6. Solve the Exacet equation (sin(y) – y sin(z)) dr + (1 +zcos(y) + cos(x)) dy = 0. ANSWER: z sin(y) +y cos(r) +y-C 7. Find an integrating factor and show that it is one (do not solve) 2r tan(y) dz + see*(y) dy = 0. ANSWER: µ = e*, → M = 2re" tan(y). N =* see°(y), M, = 2re" see"(y) - N, 8. Find an implicit general solution of the Homogeneous equation y= ANSWER: ry + In(a)- C 9. Use the substitution - (z-y) to solve y- (z- 9)² + 1. ANSWER: (z-v) 10. Solve the Bernoulli equation -y- ANSWER: Filters Add a caption. > My group
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