急!!!!!! 5 道高数题。。 回答追加100分
题目在图片里
推荐回答(6个)
1,dy/dx=x^(5/3)/y^4
<=>y^4dy=x^(5/3)dx
两边积分有y^5/5+C1=3x^(8/3)/8(C1为任意实数)
=>y=(15x^(8/3)/8-C)^(1/5)
(注:C为任意实数)
2,dy/dx=x^2e^(x^3-2)y^(1/2)
=>y^(-1/2)dy=x^2e^(x^3-2)dx
=>2y^(1/2)=∫x^2e^(x^3-2)dx
=>2y^(1/2)=e^(-2)/3∫d(e^(x^3))
=>2y^(1/2)=(e^(x^3-2))+C)/3
=>y=(e^(x^3-2))+C)^2/36(C为任意实数)
3,dy/dx=y^2/(3x^2-2x-1)
=>1/y^2dy=dx/(3x^2-2x-1)
两边积分=>-1/y=∫dx/(3x^2-2x-1)=(∫dx/(x-1))-∫dx/(3x+1))/4
=ln(x-1)/4-ln(3x+1)/12+C
=>y=1/(ln(3x+1)/12-ln(x-1)/4-C)(C为任意实数)
2
1,2y'-x^4y=3x^4
<=>2(y+3)'=x^4(y+3)<=>2(y+3)'/(y+3)=x^4
<=>(ln(y+3))'=x^4/2=>ln(y+3)=x^5/10+C=>y=e^(x^5/10+C)-3(C为任意实数)
又y(0)=e^C-3=3=>c=ln(6)=>y=e^(x^5/10+ln(6))-3
2,y'-3y/x=x^2
=>x^3*y'-3x^2*y=x^5=>(x^3*y)'=x^5=>x^3*y=x^6/6+C
=>y=x^3/6+C/x^3
y(1)=1/6+C=2=>C=11/6
=>y=x^3/6+11/(6x^3)
3,dT/dt=-k(T-Tair)
=>d(T-Tair)/dt=-k(T-Tair)
=>d(T-Tair)/(T-Tair)=-kdt
=>d(ln(T-Tair)))=-kdt=>ln(T-Tair)=-kt+C
=>T=e^(-kt+C)+Tair
接下来就好做了
4
a,z=(3+4i)/(2i-1)=1-2i
b,z^2-2iz+3=0
设z=a+bi
=>a^2-b^2+2abi-2ai+2b+3=0
=>a^2-b^2+2b+3=0 2ab-2a=0
=>z=-i或者3i
c,设z=a+bi
=>e^(a+bi)=2*e^((2kπ-π/6)i)=e^(ln2+(2kπ-π/6)i)
=>z=ln2+(2kπ-π/6)i(k为任意整数)
y''+3y'+2y=0
这是其次微分方程直接可以写出解y=Ae^(-x)+Be^(-2x)
y''+6y'+9y=0
他的特征方程式重跟所以解为y=(ax+b)e^(-3x)
第二个方程不是齐次方程
希望能帮到你!
靠,这题目太牛了,又是英文,又是高数,一般人还真不会,不过我就看着第一题像是选C,其余的感觉都太难了,光英文都没看懂 ,第4题要根据i的值来解方程
我了个去
高等数学,微积分!
解出一道我觉得我都算牛X了
哇,其实我都看不懂,可以这样跟你说吧,可能没有一个人为你这么多题得点分,你相信不。哈哈。
说实话 题目很简单都是一些最基本的东西 可惜 现在懒得些
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