Integration and Differential Equations

A) P=Ce^5t

B) P= 5e^418t

A) P=Ce^5t

B) P= 418e^5t

A) P=Ce^t

B) P= 418e^t

A) P=Ce^10t

B) P= 418e^10t

𝑦 = ln(15t)

𝑦 = 16t³

𝑦 = (2𝑡³ − 16)^1/2

𝑦 = (2𝑡³ −16)

 $\frac{3x^2}{2}$  

 $\frac{3x^2}{2}+7x+c$  

 $\frac{x^4}{8}+7x+c$  

 $\frac{x^4}{8}+c$  

 $x^{\frac{1}{2}}+c$  

 $\frac{1}{2}x^{-\frac{1}{2}}+\ c$  

 $\frac{2}{3}x^{\frac{3}{2}}+\ c$  

 $\frac{3}{2}x^{\frac{3}{2}}+\ c$  

 $x^{-1}\ +\ x^{-2}+\ c$  

 $x^0\ -\ x^{-1}+\ c$  

 $\ln x+\ x^{-1}+\ c$  

 $\ln x-\ x^{-1}+\ c$  

 $\frac{1}{3}x^3-x^2+C$  

 $x^{2\ }-2x+C$  

 $2x-2$  

 $\frac{1}{3}x^3-x^2$ 

 $6x^2+12x+C$  

 $x^{2\ }-2x+C$  

 $3x^2+6x+C$  

 $2x^3+6x^2+C$ 

 $4\cos\left(x\right)+C$  

 $-4\sin\left(-x\right)+C$  

 $4\cos\left(-x\right)+C$  

 $-4\cos\left(-x\right)+C$  

 $2x^{\frac{5}{2}}+4x^{-4x}+\ln\left|x\right|+C$  

 $5x^{\frac{1}{3}}-4e^{-4x}+1+C$  

 $\frac{5}{2}x^{\frac{3}{2}}-16e^{-4x}+\ln\left|x\right|+C$  

Got lazy with fake answers

 $2x^{\frac{5}{2}}+4x^{-4x}+\ln\left|x\right|+C$  

 $5x^{\frac{1}{3}}-4e^{-4x}+1+C$  

 $\frac{5}{2}x^{\frac{3}{2}}-16e^{-4x}+\ln\left|x\right|+C$  

Got lazy with fake answers