Download Aufgaben zu den partiellen Differentialgleichungen der by M.M. Smirnow. PDF

By M.M. Smirnow.

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Xy" = 2yy' - y' + = 0. 460. y"=xy'+y+I. 462. xy" - y' = xzyy'. In problems 463-480, reduce the order of the given equation by noting that it is homogeneous. 464. yy"=y' 2 +I5y 2 VX:- 463. xyy"-xy' 2 =yy'. 455. (x 2 + I) Solve the equation. (y' 2 - yy") = xyy'. 456. xyy"+xy' 2 =2yy'. ' 467. x 2yy"=(y-xy') 2• ,2 468. Y"+L+L=L. x x' y 459. y(xy" + y') = xy' 470. x yy" + y' 2 2 = 472. xyy" = y' (y 2 x). (I - 471. x 2(y 1 ' 0. + y'). - 2yy") = y2. 473. 4x 2y3y" = x 2 - y 4• 474. x'y'' = (y- xy')(y- xy' - x).

Y' 3 + y2 = yy' (y'+I ). 242. 244. 246. 248. 250. Solve equations 251-266 for tion by the usual methods. 8y' 3 = 27 y. y2 (y' 2 + I)= I . y' 2 = 4y 3 (1- y). yy' 3 x =I. 4(1-y)=(3y-2)2 y' 2 • + y' and then find the solu- Indicate the singular solutions if there are any. 251. y''+xy=y 2 +xy'. 253. xy' 2 - 2yy' x = 0. +x = 255. / 257. y' 2 - + 2y. 2xy' = 8x 2 • 259. y' 2 -2yy'=y 2 (ex-I). 261. 262. 263. 265. 266. + 252. xy' (xy' y) = 2y2• 254. xy' 2 = y(2y' - I). + 256. y' 3 +

X 2 (y- xy') = yy' 2• 3x' , (I + y) 2 401. y'= xa+y+I 402. y = x(y+l)-x' • 403. (y- 2xy') 2 = 4yy' 3 • 404. 6x 5y dx (y 4 In y - 3x 6 ) dy = 0. + 1,,- b- 405. y 1 = 2 vx+vy. YT· ~ 4013. 2xy'+l=y+y-l' 407. yy'+x={(x'~ 409. 410. 411. 412. 413. 414. 415. (xVy 2 +1+1)(y2 +1)dx=xydy. (x 2 + y 2 + l)yy' +

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