本次美国代写主要为微积分相关限时测试
1.(30分)考虑微分方程y0
= sin(y)。 使用方向场法绘制草图
下列每个初始条件的解:y(0)= 0,y(0)=⇡/ 4和y(0)=!⇡/ 2。
2.(30分)找到与曲线族正交的轨迹的方程式
y = ekx(k任何常数)
其中包含点(1,1)。 您无需以y = f(x)的形式给出答案。
解决方案:
单元4:练习考试1
3.(30分)找到微分方程的一般解:
y00
! 2y0
+ 2y = cos(x)
前任
解决方案:
4.(30分)使用幂级数方法,找到两个线性独立的解
2倍
y00
! 4xy0
+ 6y = 0,
解决方案:
1. (30 points) Consider the di↵erential equation y0
=sin(y). Using the method of direction fields, sketch
a solution for each of the following initial conditions: y(0) = 0, y(0) = ⇡/4 and y(0) = !⇡/2.
2. (30 points) Find an equation for the orthogonal trajectory to the family of curves
y = ekx (k any constant)
which contains the point (1, 1). You do not need to give you answer in the form y = f(x).
Solution:
Module 4: Practice Exam 1
3. (30 points) Find a general solution to the di↵erential equation:
y00
! 2y0
+2y = cos(x)
ex
Solution:
4. (30 points) Using the method of power series, find two linearly independent solutions to
x2
y00
! 4xy0
+6y =0,
Solution: