Hi,
I have a final exam soon and I couldn't solve some questions from some chapters. If you help me step by step, I really appreciate it.
Thank you
Separate. Find the general solutions of the following separable differential equation.
dy/dt=3 * sqrt(9-
^2) * sin^4(t) * cos(t)
The answer must be y= 3 * sin((3/5) * sin^5(t) + C)
Integrating Factor. Solve the following differential equations.
(dy/dt)+y=t+(e)^t y(0)=0
The answer must be y+t-1+cosht
Harmonic integral I. For what value(s) of p is the integral I=integ[1,oo] (1/(x)^p)dx convergent?
Harmonic integral II. For values of p where I is convergent, what is the value of I?
Answer must be (1^(1-p))/(p-1) when p>1.
I have a final exam soon and I couldn't solve some questions from some chapters. If you help me step by step, I really appreciate it.
Thank you
Separate. Find the general solutions of the following separable differential equation.
dy/dt=3 * sqrt(9-
^2) * sin^4(t) * cos(t)The answer must be y= 3 * sin((3/5) * sin^5(t) + C)
Integrating Factor. Solve the following differential equations.
(dy/dt)+y=t+(e)^t y(0)=0
The answer must be y+t-1+cosht
Harmonic integral I. For what value(s) of p is the integral I=integ[1,oo] (1/(x)^p)dx convergent?
Harmonic integral II. For values of p where I is convergent, what is the value of I?
Answer must be (1^(1-p))/(p-1) when p>1.