Home > Calculus > Solving Separable Differential Equations

How do I solve the equation #dy/dt = 2y - 10#?

Answer 1

You can use a technique known as Separation of Variables. Take all the #y# to one side and the #t# on the other... You get:

#dy/(2y-10)=dt#

Now you can integrate both sides with respect to the correspondent variables:

#int1/(2y-10)dy=intdt# #int1/(2(y-5))dy=intdt#

And finally #1/2ln(y-5)=t+c#

Now you can express #y# as: #ln(y-5)=2t+c# #y-5=c_1e^(2t)# where #c_1=e^c# #y=c_1e^(2t)+5#

You can substitute back to check your result (calculating #dy/dt#) remembering that now it is: #y=c_1e^(2t)+5#

By signing up, you agree to our Terms of Service and Privacy Policy

Answer 2

Cameron Alexander

To solve the equation dy/dt = 2y - 10, you can use the method of separation of variables. First, rewrite the equation as dy/dt - 2y = -10. Then, separate the variables by moving terms involving y to one side and terms involving t to the other side. Next, integrate both sides with respect to their respective variables. Finally, solve for y to find the general solution.

By signing up, you agree to our Terms of Service and Privacy Policy

Answer from HIX Tutor

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.