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d'Alembert's equation

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Davis, Harold Thayer. Introduction to nonlinear differential and integral equations. Courier Corporation, 1962.
399: 25: 523: 98: 466: 152: 54: 527: 470: 208: 366: 570: 458: 127: 36: 515: 420: 353:{\displaystyle {\frac {dx}{dp}}+{\frac {xf'(p)+g'(p)}{f(p)-p}}=0} 30: 531: 474: 58: 245:. After differentiating once, and rearranging we have 369: 254: 211: 155: 390: 352: 237: 194: 551: 494: 8: 63:introducing citations to additional sources 558: 544: 501: 487: 368: 278: 255: 253: 224: 210: 154: 53:Relevant discussion may be found on the 411: 142:, named after the French mathematician 398:, d'Alembert's equation is reduced to 7: 512: 510: 455: 453: 363:The above equation is linear. When 530:. You can help Knowledge (XXG) by 473:. You can help Knowledge (XXG) by 14: 514: 457: 46:relies largely or entirely on a 35: 592:Ordinary differential equations 577:Eponymous equations of physics 379: 373: 332: 326: 318: 312: 298: 292: 189: 183: 174: 168: 140:ordinary differential equation 1: 138:, is a first order nonlinear 195:{\displaystyle y=xf(p)+g(p)} 602:Mathematical analysis stubs 618: 597:Mathematical physics stubs 509: 452: 134:, sometimes also known as 15: 146:. The equation reads as 16:Not to be confused with 421:"d'Alembert's Equation" 238:{\displaystyle p=dy/dx} 144:Jean le Rond d'Alembert 74:"D'Alembert's equation" 587:Differential equations 526:–related article is a 469:-related article is a 392: 391:{\displaystyle f(p)=p} 354: 239: 196: 18:d'Alembert's principle 524:mathematical analysis 425:mathworld.wolfram.com 393: 355: 240: 197: 132:d'Alembert's equation 582:Mathematical physics 467:mathematical physics 367: 252: 209: 153: 59:improve this article 22:d'Alembert's formula 419:Weisstein, Eric W. 400:Clairaut's equation 136:Lagrange's equation 26:d'Alembert operator 388: 350: 235: 192: 539: 538: 482: 481: 342: 273: 124: 123: 109: 609: 560: 553: 546: 518: 511: 503: 496: 489: 461: 454: 444: 441: 435: 434: 432: 431: 416: 397: 395: 394: 389: 359: 357: 356: 351: 343: 341: 321: 311: 291: 279: 274: 272: 264: 256: 244: 242: 241: 236: 228: 201: 199: 198: 193: 119: 116: 110: 108: 67: 39: 31: 617: 616: 612: 611: 610: 608: 607: 606: 567: 566: 565: 564: 508: 507: 450: 448: 447: 442: 438: 429: 427: 418: 417: 413: 408: 365: 364: 322: 304: 284: 280: 265: 257: 250: 249: 207: 206: 151: 150: 120: 114: 111: 68: 66: 52: 40: 29: 12: 11: 5: 615: 613: 605: 604: 599: 594: 589: 584: 579: 569: 568: 563: 562: 555: 548: 540: 537: 536: 519: 506: 505: 498: 491: 483: 480: 479: 462: 446: 445: 436: 410: 409: 407: 404: 387: 384: 381: 378: 375: 372: 361: 360: 349: 346: 340: 337: 334: 331: 328: 325: 320: 317: 314: 310: 307: 303: 300: 297: 294: 290: 287: 283: 277: 271: 268: 263: 260: 234: 231: 227: 223: 220: 217: 214: 203: 202: 191: 188: 185: 182: 179: 176: 173: 170: 167: 164: 161: 158: 122: 121: 57:. Please help 43: 41: 34: 13: 10: 9: 6: 4: 3: 2: 614: 603: 600: 598: 595: 593: 590: 588: 585: 583: 580: 578: 575: 574: 572: 561: 556: 554: 549: 547: 542: 541: 535: 533: 529: 525: 520: 517: 513: 504: 499: 497: 492: 490: 485: 484: 478: 476: 472: 468: 463: 460: 456: 451: 440: 437: 426: 422: 415: 412: 405: 403: 401: 385: 382: 376: 370: 347: 344: 338: 335: 329: 323: 315: 308: 305: 301: 295: 288: 285: 281: 275: 269: 266: 261: 258: 248: 247: 246: 232: 229: 225: 221: 218: 215: 212: 186: 180: 177: 171: 165: 162: 159: 156: 149: 148: 147: 145: 141: 137: 133: 129: 118: 107: 104: 100: 97: 93: 90: 86: 83: 79: 76: –  75: 71: 70:Find sources: 64: 60: 56: 50: 49: 48:single source 44:This article 42: 38: 33: 32: 27: 23: 19: 532:expanding it 521: 475:expanding it 464: 449: 439: 428:. Retrieved 424: 414: 362: 204: 135: 131: 125: 112: 102: 95: 88: 81: 69: 45: 128:mathematics 571:Categories 430:2024-06-02 406:References 115:April 2024 85:newspapers 336:− 55:talk page 309:′ 289:′ 99:scholar 24:or the 205:where 101:  94:  87:  80:  72:  522:This 465:This 106:JSTOR 92:books 528:stub 471:stub 78:news 126:In 61:by 573:: 423:. 402:. 130:, 20:, 559:e 552:t 545:v 534:. 502:e 495:t 488:v 477:. 433:. 386:p 383:= 380:) 377:p 374:( 371:f 348:0 345:= 339:p 333:) 330:p 327:( 324:f 319:) 316:p 313:( 306:g 302:+ 299:) 296:p 293:( 286:f 282:x 276:+ 270:p 267:d 262:x 259:d 233:x 230:d 226:/ 222:y 219:d 216:= 213:p 190:) 187:p 184:( 181:g 178:+ 175:) 172:p 169:( 166:f 163:x 160:= 157:y 117:) 113:( 103:· 96:· 89:· 82:· 65:. 51:. 28:.

Index

d'Alembert's principle
d'Alembert's formula
d'Alembert operator

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introducing citations to additional sources
"D'Alembert's equation"
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ordinary differential equation
Jean le Rond d'Alembert
Clairaut's equation
"d'Alembert's Equation"
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t
e
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mathematical analysis
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