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at all. SECTION 1.2 EXERCISES In Probiems i-10 determine a region of the xy-plane for which the given differential equation would have a unique solution through a point (Xp, yo} firSt in the region. dy dy 2. dx dy dx dy 4. dx

at all. SECTION 1.2 EXERCISES In Probiems i-10 determine a region of the xy-plane for which the given differential equation would have a unique solution through a point (Xp, yo} firSt in the region. dy dy 2. dx dy dx dy 4. dx

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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at all. SECTION T.2 EXERCISES as In Probiems 1-10 determine a region of the xy-plane for which the given differential equation would have a unique solution through a point (X,, Yo} in the region. h ax 2. Vxy dy y dx dy %3D dx
Transcribed Image Text:at all. SECTION T.2 EXERCISES as In Probiems 1-10 determine a region of the xy-plane for which the given differential equation would have a unique solution through a point (X,, Yo} in the region. h ax 2. Vxy dy y dx dy %3D dx
iven differential equation. In some cases assume an appropriate interval al equation xy(9) – xy" + 4xy'-3y = 0 nt we have n function al with sys x? dy + (y-xy - xe) dx = 0 d'y + 9y = = sin y 6. more unkno and y den dy following 1 dr? d'y dx d'r 8. = - dx dr? (sin x)y" - (cos x)y' Problems 11-40 verify that the indicated function is a solution of the = 2 10. (1- y?) dx + x dy = 0 validity for the solution. Where used, the symbols c, and c, denote con- ants. 1. 2y' +y = 0; y e-2 12. y' + 4y = 32; y = 8 ple functid dy tem on soi 2y e: y = er + 10e?* dx dy 14. + 20y = 24; y = - e-01 dt y' = 25 + y; y = 5 tan 5x dy : y= (Vx + c), x > 0, c > 0 V x dx ations are o need to . y' + y = sin x; y = sin x- cos x + 10e * erms of *. B. 2xy dx + (x + 2y) dy = 0; x'y + y = er y in term nd 20 (y') + xy' = y; y = x+ 1 1 e differentio. x dy + 2xy dx = 0; y = example. A fferentiab1. y = 2xy' + y(y')': y? = c(x + c;) ve may r2. y' = 2Viyl: y = xx algebra. icit solutid3. y' y = 1; y=x In x, x>0 - - quation f of symb4. aC;e 1+ bcet 2- X dP P(a -- bP); P = dt dX 5. dt 3(2-X)(1-X); in 1 - n is linc, y' + 2xy = 1; y=eedt + ce +Ge On is lined, = 0: C(x +y) = re 7. (x+ y) dx + (x - xy) dy y = 0 8. y" + y'- 12y = 0; y Ce+ Ce 9. y" - 6y' + 13y = 0; y = e cos 2x
Transcribed Image Text:iven differential equation. In some cases assume an appropriate interval al equation xy(9) – xy" + 4xy'-3y = 0 nt we have n function al with sys x? dy + (y-xy - xe) dx = 0 d'y + 9y = = sin y 6. more unkno and y den dy following 1 dr? d'y dx d'r 8. = - dx dr? (sin x)y" - (cos x)y' Problems 11-40 verify that the indicated function is a solution of the = 2 10. (1- y?) dx + x dy = 0 validity for the solution. Where used, the symbols c, and c, denote con- ants. 1. 2y' +y = 0; y e-2 12. y' + 4y = 32; y = 8 ple functid dy tem on soi 2y e: y = er + 10e?* dx dy 14. + 20y = 24; y = - e-01 dt y' = 25 + y; y = 5 tan 5x dy : y= (Vx + c), x > 0, c > 0 V x dx ations are o need to . y' + y = sin x; y = sin x- cos x + 10e * erms of *. B. 2xy dx + (x + 2y) dy = 0; x'y + y = er y in term nd 20 (y') + xy' = y; y = x+ 1 1 e differentio. x dy + 2xy dx = 0; y = example. A fferentiab1. y = 2xy' + y(y')': y? = c(x + c;) ve may r2. y' = 2Viyl: y = xx algebra. icit solutid3. y' y = 1; y=x In x, x>0 - - quation f of symb4. aC;e 1+ bcet 2- X dP P(a -- bP); P = dt dX 5. dt 3(2-X)(1-X); in 1 - n is linc, y' + 2xy = 1; y=eedt + ce +Ge On is lined, = 0: C(x +y) = re 7. (x+ y) dx + (x - xy) dy y = 0 8. y" + y'- 12y = 0; y Ce+ Ce 9. y" - 6y' + 13y = 0; y = e cos 2x
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