Calculus

posted by .

dy/dx = 4ye^(5x)

a) Separate the differential equation, then integrate both sides.

b) Write the general solution as a function y(x).

For the second part, I got y(x)=e^((5e^(5x))/(5)) + C but I don't understand how to separate differential equations and/or integrate both sides...

  • Calculus -

    dy / y = 4 e^(5x) dx

    ln y = (4/5) e^(5x) + c

    e^ln y = y = e^ [(4/5)e^(5x) +c)

    y = e^c e^[(4/5)e^(5x) ]

    y = C e^[(4/5)e^(5x) ]

Respond to this Question

First Name
School Subject
Your Answer

Similar Questions

  1. Differential Equations

    Find the general solution of the differential equation specified. 1) dy/dt= 1/(ty+1+y+1) 2) dy/dx=sec y I got y(x)=arcsin(x) for the second one. I'm not sure what to do with the first one.
  2. calculus-differential equation

    Consider the differential equation: (du/dt)=-u^2(t^3-t) a) Find the general solution to the above differential equation. (Write the answer in a form such that its numerator is 1 and its integration constant is C). u=?
  3. Math

    dz =(−sinx + 2xy^2)dx +(2x^2 y)dy Integrate the differential to find the function z. Would I say that z was equal to two separate differentials and integrate the first part of the function with respect to x and the second part …
  4. calculus

    Please help. How do I separate the variables in the following differential equation dy/dx=(2/27)(x-3)then square root (x^2-6x+23)/y where (y>0). Then give general solution in implicit form. Thank you so much if you can help.
  5. calculus

    verify that y=c/x^2 is a general solution of the differential equation y'+(2/x) y=0-6y=0 then find a particular solution of the differential equation that satisfies the side condition y(1)=2
  6. Differential Equations

    Consider the differential equation: dy/dt=y/t^2 a) Show that the constant function y1(t)=0 is a solution. b)Show that there are infinitely many other functions that satisfy the differential equation, that agree with this solution when …
  7. Differential Equations

    Consider the differential equation: dy/dt=y/t^2 a) Show that the constant function y1(t)=0 is a solution. b)Show that there are infinitely many other functions that satisfy the differential equation, that agree with this solution when …
  8. Differential Equations

    Consider the differential equation: dy/dt=y/t^2 a) Show that the constant function y1(t)=0 is a solution. b)Show that there are infinitely many other functions that satisfy the differential equation, that agree with this solution when …
  9. calculus

    calculus. suppose dR/dt= (d/R)^(2) and P(1) 4. separate the differential equation, integrate both sides
  10. Calculus

    Hello, I would greatly appreciate any help that I can have with the following calculus question below. It has to do with separable differential equations. I'm also going to explain what I've done so far, so please bear with me (but …

More Similar Questions