Chapter 9
Applied Calculus: For Business, Economics, and the Social and Life Sciences · 22 exercises
Problem 1
$$ \frac{d y}{d x}=x^{3}-3 x^{2}+5 $$ 2\. \(\frac{d y}{d x}=0.02 y\)
5 step solution
Problem 4
\(\frac{d y}{d x}=y(1-y)\)
8 step solution
Problem 6
\(\frac{d y}{d x}=y e^{-2 x}\)
5 step solution
Problem 8
\(\frac{d y}{d x}+\frac{y}{x}=\frac{2}{x+1}\)
8 step solution
Problem 9
\(\frac{d y}{d x}+\frac{2 y}{x+1}=\frac{4}{x+2}\)
7 step solution
Problem 11
\(\frac{d y}{d x}=\frac{\ln x}{x y}\)
4 step solution
Problem 12
\(\frac{d y}{d x}=e^{2 x-y}\)
3 step solution
Problem 13
\(\frac{d y}{d x}=5 x^{4}-3 x^{2}-2 ; y=4\) when \(x=1\)
5 step solution
Problem 14
\(\frac{d y}{d x}=3-y ; y=2\) when \(x=0\)
6 step solution
Problem 15
\(\frac{d y}{d x}=0.06 y ; y=100\) when \(x=0\)
5 step solution
Problem 16
\(\frac{d y}{d x}-\frac{y}{x}=\frac{2}{x}, y=-1\) when \(x=1\)
8 step solution
Problem 18
\(\frac{d y}{d x}+\frac{y}{x+1}=x, y=0\) when \(x=3\)
8 step solution
Problem 20
\(\frac{d y}{d x}+3 x^{2} y=x^{2} ; y=2\) when \(x=0\)
8 step solution
Problem 21
\(\frac{d y}{d x}=y \ln \sqrt{x} ; y=-4\) when \(x=1\)
7 step solution
Problem 22
\(\frac{d y}{d x}=\frac{\ln x}{y} ; y=100\) when \(x=1\)
4 step solution
Problem 24
\(\frac{d^{2} y}{d x^{2}}=2 ; y=5\) and \(\frac{d y}{d x}=3\) when \(x=0\)
5 step solution
Problem 26
\(y_{n}=-8 y_{n-1} ; y_{0}=1\)
6 step solution
Problem 27
\(y_{n}-y_{n-1}=3 ; y_{0}=1\)
5 step solution
Problem 29
\(y_{n}-5 y_{n-1}=2 ; y_{0}=2\)
6 step solution
Problem 30
\(y_{n}-2 y_{n-1}=8 ; y_{0}=-1\)
4 step solution
Problem 34
\(y^{\prime}=\frac{x-y}{x+y} ;(1,1)\)
8 step solution
Problem 36
\(y^{\prime}=\frac{x y}{x^{2}+y^{2}},(0,1)\)
6 step solution