Question

Consider the first order separable equation y′=12x^3y(1+2x^4)^1/2. An implicit general solution can be written in the...

Consider the first order separable equation y′=12x^3y(1+2x^4)^1/2. An implicit general solution can be written in the form y=Cf(x) for some function f(x) with C an arbitrary constant. Here f(x)= Next find the explicit solution of the initial value problem y(0)=1

y=

Math   Advanced-Math   
0 0
Add a commentTranscribed image text
Next >

Homework Answers

Answer #1

0 0
Know the answer?
Your Answer:

Post as a guest

Your Name:

What's your source?

Earn Coins

Coins can be redeemed for fabulous gifts.

Log In

Sign Up

Not the answer you're looking for?
Ask your own homework help question
Similar Questions
The differential equation dydx=72/(y^1/4+64x^2y^1/4) has an implicit general solution of the form F(x,y)=K, where K is...
The differential equation dydx=72/(y^1/4+64x^2y^1/4) has an implicit general solution of the form F(x,y)=K, where K is an arbitrary constant. In fact, because the differential equation is separable, we can define the solution curve implicitly by a function in the form F(x,y)=G(x)+H(y)=K Find such a solution and then give the related functions requested. F(x,y)=G(x)+H(y)=
A) In this problem we consider an equation in differential form ???+???=0Mdx+Ndy=0. The equation (5?^4?+4cos(2?)?^−4)??+(5?^5−3?^−4)??=0 in...
A) In this problem we consider an equation in differential form ???+???=0Mdx+Ndy=0. The equation (5?^4?+4cos(2?)?^−4)??+(5?^5−3?^−4)??=0 in differential form ?˜??+?˜??=0 is not exact. Indeed, we have My-Mx= ________ 5x^4-4(4)cos(2x)*y^(-5)-25x^4 (My-Mn)/M=_____ -4/y in function y alone. ?(?)= _____y^4 Multiplying the original equation by the integrating factor we obtain a new equation ???+???=0 where M=____ N=_____ which is exact since My=_____ Nx=______ This problem is exact. Therefore an implicit general solution can be written in the form  ?(?,?)=? where ?(?,?)=_________ Finally find the value...
Notice that ?y/?x = (3y+2x)/(x+y) is not separable. However, we can solve the equation with the...
Notice that ?y/?x = (3y+2x)/(x+y) is not separable. However, we can solve the equation with the following steps. a. Define a new variable z=y/x and express ?y/?x in terms of only ? and ?z/?x
In this problem we consider an equation in differential form ???+???=0 The equation (6?^(1/?)+4?^3?^−3)??+(6?^2?^−2+4)??=0 in differential...
In this problem we consider an equation in differential form ???+???=0 The equation (6?^(1/?)+4?^3?^−3)??+(6?^2?^−2+4)??=0 in differential form ?˜??+?˜??=0 is not exact. Indeed, we have ?˜?−?˜?/M=______ is a function of ? alone. Namely we have μ(y)= Multiplying the original equation by the integrating factor we obtain a new equation ???+???=0 ?=____ ?=_____ Which is exact since ??=______ ??=_______ are equal. This problem is exact. Therefore an implicit general solution can be written in the form  ?(?,?)=?F where ?(?,?)=__________
Find the general solution of the system dx/dt = 2x + 3y dy/dt = 5y Determine...
Find the general solution of the system dx/dt = 2x + 3y dy/dt = 5y Determine the initial conditions x(0) and y(0) such that the solutions x(t) and y(t) generates a straight line solution. That is y(t) = Ax(t) for some constant A.
For a real number "a", consider the system of equations: x+y+z=2 2x+3y+3z=4 2x+3y+(a^2-1)z=a+2 Which of the...
For a real number "a", consider the system of equations: x+y+z=2 2x+3y+3z=4 2x+3y+(a^2-1)z=a+2 Which of the following statements is true? A. If a= 3 then the system is inconsistent. B. If a= 1 then the system has infinitely many solutions. C. If a=−1 then the system has at least two distinct solutions. D. If a= 2 then the system has a unique solution. E. If a=−2 then the system is inconsistent.
solve for y: 1. dy/dx= xe^y separable 2. x(dy/dx)+3y=x^2 when y(5)=0 1st order linear
solve for y: 1. dy/dx= xe^y separable 2. x(dy/dx)+3y=x^2 when y(5)=0 1st order linear
1) Find the equation of the line that psses through the vertex if the parabola f(x)=2x^2-12x+19...
1) Find the equation of the line that psses through the vertex if the parabola f(x)=2x^2-12x+19 and that crosses the x-axis at x=5 2) Find the equation of the line that passes through the certex of the parabala f(x)=3x^2-12x+17 and has y-intercept of (0,10)
1) Basic Euler’s Method: y'+xysin/y+1 y(0)=1 a) What is the initial condition? b) What order is...
1) Basic Euler’s Method: y'+xysin/y+1 y(0)=1 a) What is the initial condition? b) What order is this differential equation? c) Is this an autonomous differential equation? d) Is this a separable differential equation? e) Find the general solution to the given differential equation, by hand. You will not be able to completely solve for y(x) – that’s ok. Write out all your work and attach it to your Questions tab. f) Using the initial condition, solve the initial value problem...
Consider the initial value problem dy dx = 1−2x 2y , y(0) = − √2 (a)...
Consider the initial value problem dy dx = 1−2x 2y , y(0) = − √2 (a) (6 points) Find the explicit solution to the initial value problem. (b) (3 points) Determine the interval in which the solution is defined.
ADVERTISEMENT
Need Online Homework Help?

Get Answers For Free
Most questions answered within 1 hours.

Ask a Question
ADVERTISEMENT