大一高数！这个方程怎么解出y？∫ ydx这一部一般怎么解？急在线等！ 高数微分方程，怎么用 常数变易法 做这题？我不要直接用公式法...
\u5927\u5b66\u6570\u5b66\u4e2d\u7b26\u53f7exp()\u662f\u4ec0\u4e48\u610f\u601d\u554a\uff1f\u6025\uff01\u5728\u7ebf\u7b49\u7b26\u53f7exp\u662f\u9ad8\u7b49\u6570\u5b66\u4e2d\u8868\u793a\u4ee5\u81ea\u7136\u5e38\u6570e\u4e3a\u5e95\u7684\u6307\u6570\u51fd\u6570\u3002
\u901a\u4fd7\u6765\u8bb2\uff0cexp()\u8868\u793a\u7684\u542b\u4e49\u5c31\u662fe\u7684\u51e0\u6b21\u65b9\uff0c\u6bd4\u5982exp(3)\u5c31\u8868\u793ae³\u3002
\u6269\u5c55\u8d44\u6599\uff1a
exp\u5728\u4e0d\u540c\u884c\u4e1a\u7684\u89e3\u91ca\uff1a
1\u3001\u5316\u5b66\u5242
\u4e00\u79cd\u5316\u5b66\u6742\u4ea4\u5242\uff0c\u4e3b\u8981\u6210\u5206\u78fa\u9170\u8132\u7c7b\u5316\u5408\u7269\uff0c\u4f5c\u7528\u9776\u6807\u662f\u690d\u7269\u7684\u4e59\u9170\u4e73\u9178\u5408\u6210\u9176\uff08acetolactate synthase\uff0cALS\uff09\uff0c\u901a\u8fc7\u6291\u5236\u9176\u6d3b\u6027\uff0c\u963b\u6b62\u652f\u94fe\u6c28\u57fa\u9178\u7f2c\u6c28\u9178\u3001\u4eae\u6c28\u9178\u548c\u5f02\u4eae\u6c28\u9178\u7684\u5408\u6210\u3002
2\u3001\u4f9b\u5e94\u5546
Expedition\uff08\u7b80\u79f0\uff1aEXP) \uff1a\u662f\u4e16\u754c\u8457\u540d\u9879\u76ee\u7ba1\u7406\u8f6f\u4ef6\u4f9b\u5e94\u5546- - -\u7f8e\u56fdPrimavera\u516c\u53f8\u7684\u4e3b\u8981\u4ea7\u54c1\u4e4b\u4e00\uff0c\u662f\u56fd\u9645\u89c4\u8303\u7684\u65bd\u5de5\u7ba1\u7406\u548c\u5408\u540c\u53ca\u5efa\u8bbe\u4fe1\u606f\u7ba1\u7406\u8f6f\u4ef6\uff0c\u5b83\u5b8c\u5168\u6309FIDIC\u7684\u5408\u540c\u7ba1\u7406\u6a21\u5f0f\u4ee5\u5408\u540c\u7ba1\u7406\u4e3a\u4e2d\u5fc3\u6709\u673a\u5730\u7ba1\u7406\u5408\u540c\u7684\u5c65\u884c\u8fc7\u7a0b\uff0c\u5b83\u5168\u9762\u5f52\u7eb3\u4e86\u5efa\u8bbe\u9879\u76ee\u5408\u540c\u7ba1\u7406\u7684\u4e8b\u52a1\u3002
\u901a\u8fc7\u4e1a\u52a1\u68b3\u7406\uff0c\u5206\u7c7b\u7edf\u8ba1\uff0c\u5173\u8054\u7ba1\u7406\uff0c\u8ddf\u8e2a\u50ac\u529e\uff0c\u4f7f\u5f97\u539f\u672c\u6563\u843d\u5728\u5404\u4e2a\u90e8\u95e8\u548c\u5404\u4e2a\u4eba\u6848\u5934\uff0c\u67dc\u5b50\u4e2d\u7684\u6240\u6709\u5408\u540c\u53f0\u5e10\uff0c\u8d39\u7528\u5f80\u6765\uff0c\u6587\u4ef6\u5f80\u6765\uff0c\u8fdb\u5ea6\u6b3e\u4ed8\u6b3e\u51ed\u8bc1\uff0c\u53d8\u66f4\u53ca\u5176\u5904\u7406\u8fc7\u7a0b\u8bb0\u5f55\uff0c\u65bd\u5de5\u56fe\u7eb8\u8bb0\u5f55\u7b49\u7b49\uff0c\u7edf\u7edf\u6709\u6761\u4e0d\u7d0a\u5730\u8bb0\u8f7d\u5230Expedition\u8f6f\u4ef6\u4e2d\uff1b\u4f7f\u4e00\u5207\u53d8\u5f97\u6709\u7ae0\u53ef\u5faa.
3\u3001\u884c\u4e1a\u8f6f\u4ef6
\u884c\u4e1a\u8f6f\u4ef6\u7684\u9ad8\u7ea7\u4e13\u5bb6\u7248\uff0c\u5728\u7075\u6d3b\u6027\u548c\u529f\u80fd\u4e0a\u6bd4\u4e13\u4e1a\u7248\uff08pro\uff09\u66f4\u52a0\u5f3a\u5927\uff0c\u4e5f\u66f4\u52a0\u590d\u6742\u3002
exploit\uff08\u7b80\u79f0EXP\uff09\uff0c\u5b83\u5728\u9ed1\u5ba2\u773c\u91cc\u5c31\u662f\u6f0f\u6d1e\u5229\u7528\u3002\u4e00\u822c\u6307\u6f0f\u6d1e\u5229\u7528\u7a0b\u5e8f\u3002
\u53c2\u8003\u8d44\u6599\u6765\u6e90\uff1a\u767e\u5ea6\u767e\u79d1=exp
\u3002
绛旓細y''|y=y2* + p(x)y'|y=y2* +q(x)y|y=y2* =f(x) (2)娉細y''|y=y1* 琛ㄧずy鐨勫煎彇y1*锛涳紙1锛-锛2锛夊彲寰 y1*-y2*鏄痽'' + p(x)y' +q(x)y=0鐨勮В锛屼笉鏄潪榻愭鏂圭▼瑙锛涜岋紙1锛+锛2锛夊彲寰 (y1*+y2*)/2鏄痽'' + p(x)y' +q(x)y=f(x)鐨...
绛旓細涓鑸潵璇达紝瑙ｈ繖绉鏂圭▼鐨勬柟娉曪紝甯稿父鏄敤位浣滀负妗ユ锛屾潵娑堝幓x鎴杫鎴杬锛屾渶缁堣В鍑猴紙x锛寉锛寊锛夛紝鑰岃В鍑何荤殑鍊煎苟涓嶉偅涔堥噸瑕併傛湰棰橈細浠庘憽寰楀埌位= -2z/y鈽咃紝浠庘憿寰楀埌位=锛4+y锛/2z鈽呪槄锛屼粠鈽=鈽呪槄锛屽緱鍒4zz= -4y-yy鈽呪槄鈽咃紝鎶娾槄鈽呪槄浠ｅ叆鈶ｏ紝寰楀埌鍏充簬鈥測鈥濈殑鏂圭▼锛屼粠涓瑙ｅ嚭y銆傘傘
绛旓細鐗瑰緛鏂圭▼涓簉^2-5r+6=0 瑙ｅ緱鐗瑰緛鏍箁1,2=2,3 鎵浠ラ綈娆℃柟绋嬬殑閫氳В涓簓1=c1e^(2x)+c2e^(3x)璁剧壒瑙2=x(px+q)e^2x 甯﹀叆鍘鏂圭▼瑙寰梡=0, q= -3 鎵浠2=-3xe^(2x)鎵浠ラ氳Вy=y1+y2=(c1-3x)e^(2x)+c2e^(3x)
绛旓細瑙ｏ細鏂圭▼涓よ竟鍚岄櫎浠锛屽緱鍒颁竴涓綈娆℃柟绋 y'+y/x=2鈭歽/x 浠=y/x,dy/dx=u+xdu/dx;鍒欏彲浠ュ緱鍒 u+xdu/dx+u=2鈭歶 鍒嗙鍙橀噺寰楀埌 du/(2鈭歶-2u)=dx/x 涓よ竟鍚屾椂绉垎锛屽彲浠ュ緱鍒 -ln|1-鈭歶|=ln|x|+c
绛旓細1. 涓闃跺父绯绘暟绾挎ч潪榻愭鏂圭▼ 榻愭閫氳В涓y=e^x 鐗硅В璁句负y=ax骞虫柟锛媌x+c y'=2ax+b 2ax+b-ax骞虫柟-bx-c=x^2 -ax^2+(2a-b)x+b-c=x^2 -a=1 2a-b=0 b-c=0 鎵浠 a=-1 b=-2 c=-2 鐗硅В涓簓=-x^2-2x-2 閫氳В涓簓=ce^x-x^2-2x-2 2. 浜岄樁甯哥郴鏁伴綈娆＄嚎鎬ф柟绋 r...
绛旓細鍗硃²=4鈭(y³)+c₁锛涒埓p=dy/dx=鈭歔4鈭(y³)+c₁];浠ｅ叆鍒濆鏉′欢寰梒₁=0; 鏁卍y/dx=2y^(3/4)锛泍^(-3/4)dy=2dx锛涚Н鍒嗕箣寰楋細4y^(1/4)=2x+c₂锛涗唬鍏ュ垵濮嬫潯浠跺緱c₂=0; 鈭磞=(1/16)x^4.(2).瑙ｏ細榻愭鏂圭▼ y''-2y'-3y=0...
绛旓細濡傚浘
绛旓細娑堝厓鎴栭檷娆°傛湰鏂圭▼缁勶紝鍑忔硶鍚庡洜寮忓垎瑙ｈ岄檷娆★紝鍘熸柟绋嬬粍鍖栦负涓や釜鏂圭▼缁(涓涓柟绋嬫槸涓娆★紝鍙︿竴涓柟绋嬫槸涓ゆ)銆傛弧鎰忥紝璇峰強鏃堕噰绾炽傝阿璋紒
绛旓細1. y'' - y' = 1, 鐗瑰緛鏂圭▼ r^2-r = 0, r = 0, 1.鐗硅В搴旇涓 y = ax锛 浠ｅ叆寰垎鏂圭▼寰 a = -1锛屽垯鍘熷井鍒嗘柟绋嬬殑閫氳В鏄 y = C1+C2e^x -ax.2. z = xy,(1) 璁 F = xy-z锛 鍒 Fx = y, Fy = x, Fz = 1 鍦ㄧ偣M(1, 1, 1), Fx = 1,...
绛旓細鍐嶄护 \( x = 0 \)锛孿( y = 0 \) 浠ｅ叆寰楃煡 \( C = 0.5 \)锛屽洜姝よВ涓 \( y = 0.5(e^x + sin x - cos x) \)銆4銆佸井鍒鏂圭▼ \( y' + \frac{1 - 2x}{x^2}y = 1 \)锛屽嵆 \( \left(\frac{e^{-1/x - 2\ln x}}{x^2}\right)y \) 鐨勫鏁颁负 \( e^{...
