How do you solve for the equation dy/dx=3x^2/e^2y that satisfies the initial condition f(0)=12?

sooxicyiy 2022-09-14 Answered
How do you solve for the equation d y d x = 3 x 2 e 2 y that satisfies the initial condition f(0)=12?
You can still ask an expert for help

Expert Community at Your Service

  • Live experts 24/7
  • Questions are typically answered in as fast as 30 minutes
  • Personalized clear answers
Learn more

Solve your problem for the price of one coffee

  • Available 24/7
  • Math expert for every subject
  • Pay only if we can solve it
Ask Question

Answers (1)

Hofpoetb9
Answered 2022-09-15 Author has 17 answers
First of all, I think ther is a mistake in your writing, I think you wanted to write:
d y d x = 3 x 2 e 2 y
This is a separable differential equations, so:
e 2 y d y = 3 x 2 d x e 2 y d y = 3 x 2 d x
1 2 e 2 y = x 3 + c .
Now to find c let's use the condition: f ( 0 ) = 1 2
1 2 e 2 1 2 = 0 3 + c c = 1 2 e
So the solution is:
1 2 e 2 y = x 3 + 1 2 e e 2 y = 2 x 3 + e 2 y = ln ( 2 x 3 + e )
y = 1 2 ln ( 2 x 3 + e )
Not exactly what you’re looking for?
Ask My Question

Expert Community at Your Service

  • Live experts 24/7
  • Questions are typically answered in as fast as 30 minutes
  • Personalized clear answers
Learn more

You might be interested in

asked 2020-11-23

Write an equivalent first-order differential equationand initial condition for y y=1+0xy(t)dt

asked 2022-07-13
I have difficulties to solve these two differential equations:
1) y ( x ) = x y ( x ) x + y ( x ) with the initial condition y ( 1 ) = 1 .I'm arrived to prove that
y = x ( 2 e 2 ( ln x + c ) 1 )
but I don't know if it's correct. If it's right, how do I find the constant c? Because WolframAlpha says that the solution is y ( x ) = 2 x 2 + 1 x.
2) y ( x ) = 2 y ( x ) x 2 x y ( x ) . I'm arrived to prove that z 1 ( z + 1 ) 3 = e 2 c x 2 but I don't know if it's correct. If it's right, how do I explain z to substitute it in y = x z? Then, how do I find the constant c ?
asked 2022-09-09
What is the particular solution of the differential equation y + y tan x = sin ( 2 x ) where y(0)=1?
asked 2021-05-05

If f(x)+x2[f(x)]5=34 and f(1)=2, find f(1).

asked 2022-05-21
In studying a reflection-transmission problem involving exotic materials, I have come across the following linear first-order differential equation:
(1) A t g ( t ) + B g ( t ) = f ( t ) ,
where A and B are constants, g(t) is associated with the reflected wave, and f(t) is a (finite) driving function associated with the incident wave. Both A and B may be positive or negative. I am interested in the behavior of the solution in the limit that A 0
In studying a reflection-transmission problem involving exotic materials, I have come across the following linear first-order differential equation:A∂∂tg(t)+Bg(t)=f(t),(1)where A and B are constants, g(t) is associated with the reflected wave, and f(t) is a (finite) driving function associated with the incident wave. Both A and B may be positive or negative. I am interested in the behavior of the solution in the limit that A\rightarrow0.
I know there is an exact solution to Eq. (1), which is
g ( t ) = C e B t / A + 1 A t e B ( t t ) / A f ( t ) d t ,
where C=0 because g(t)=0 if f(t)=0. However, I do not understand how this exact solution reduces to the case where A=0, which is g ( t ) = B 1 f ( t ). Any insight would be greatly appreciated.
I've seen a lot of documents discussing asymptotic analyses of linear differential equations, but they all start with second-order equations. Is this because there is inherently problematic with first-order?
asked 2022-09-14
What is a solution to the differential equation d y d x = 2 csc 2 x cot x ?
asked 2021-09-20
Evaluate the indefinite integral as an infinite series. cosx1xdx