Question

A Bernoulli differential equation is one of the form dxdy+P(x)y=Q(x)yn Observe that, if n=0 or 1,...

A Bernoulli differential equation is one of the form dxdy+P(x)y=Q(x)yn

Observe that, if n=0 or 1, the Bernoulli equation is linear. For other values of n, the substitution u=y^(1−n) transforms the Bernoulli equation into the linear equation du/dx+(1−n)P(x)u=(1−n)Q(x)

Use an appropriate substitution to solve the equation y'−(3/x)y=y^4/x^2 and find the solution that satisfies y(1)=1

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
A Bernoulli differential equation is one of the form dy/dx+P(x)y=Q(x)y^n (∗) Observe that, if n=0 or...
A Bernoulli differential equation is one of the form dy/dx+P(x)y=Q(x)y^n (∗) Observe that, if n=0 or 1, the Bernoulli equation is linear. For other values of n, the substitution u=y^(1−n) transforms the Bernoulli equation into the linear equation du/dx+(1−n)P(x)u=(1−n)Q(x). Consider the initial value problem xy′+y=−8xy^2, y(1)=−1. (a) This differential equation can be written in the form (∗) with P(x)=_____, Q(x)=_____, and n=_____. (b) The substitution u=_____ will transform it into the linear equation du/dx+______u=_____. (c) Using the substitution in part...
(1 point) A Bernoulli differential equation is one of the form dydx+P(x)y=Q(x)yn     (∗) Observe that, if n=0...
(1 point) A Bernoulli differential equation is one of the form dydx+P(x)y=Q(x)yn     (∗) Observe that, if n=0 or 1, the Bernoulli equation is linear. For other values of n, the substitution u=y1−n transforms the Bernoulli equation into the linear equation dudx+(1−n)P(x)u=(1−n)Q(x).dudx+(1−n)P(x)u=(1−n)Q(x). Consider the initial value problem y′=−y(1+9xy3),   y(0)=−3. (a) This differential equation can be written in the form (∗) with P(x)= , Q(x)= , and n=. (b) The substitution u= will transform it into the linear equation dudx+ u= . (c) Using...
Solve the Bernoulli differential equation. The Bernoulli equation is a well-known nonlinear equation of the form...
Solve the Bernoulli differential equation. The Bernoulli equation is a well-known nonlinear equation of the form y' + P(x)y = Q(x)yn that can be reduced to a linear form by a substitution. The general solution of a Bernoulli equation is y1 − ne∫(1 − n)P(x) dx = (1 − n)Q(x)e∫(1 − n)P(x) dx dx + C. (Enter your solution in the form F(x, y) = C or y = F(x, C) where C is a needed constant.) y' − 10y...
Solve the Bernoulli differential equation. The Bernoulli equation is a well-known nonlinear equation of the form...
Solve the Bernoulli differential equation. The Bernoulli equation is a well-known nonlinear equation of the form y' + P(x)y = Q(x)yn that can be reduced to a linear form by a substitution. The general solution of a Bernoulli equation is y1 − ne∫(1 − n)P(x) dx = (1 − n)Q(x)e∫(1 − n)P(x) dx dx + C. (Enter your solution in the form F(x, y) = C or y = F(x, C) where C is a needed constant.) y8y' − 5y9...
(1 point) Given the following differential equation (x2+2y2)dxdy=1xy, (a) The coefficient functions are M(x,y)= and N(x,y)=...
(1 point) Given the following differential equation (x2+2y2)dxdy=1xy, (a) The coefficient functions are M(x,y)= and N(x,y)= (Please input values for both boxes.) (b) The separable equation, using a substitution of y=ux, is dx+ du=0 (Separate the variables with x with dx only and u with du only.) (Please input values for both boxes.) (c) The solution, given that y(1)=3, is x= Note: You can earn partial credit on this problem. I just need part C. thank you
Consider the Bernoulli equation dy/dx + y = y^2, y(0) = −1 Perform the substitution that...
Consider the Bernoulli equation dy/dx + y = y^2, y(0) = −1 Perform the substitution that turns this equation into a linear equation in the unknown u(x). Solve the equation for u(x) using the Laplace transform. Obtain the original solution y(x). Does it sound familiar?
solve the given differential equation by using an appropriate substitution. The DE is a Bernoulli equation....
solve the given differential equation by using an appropriate substitution. The DE is a Bernoulli equation. x * dy/dx + y = 1/y^2
(1 point) Given the following initial value problem (x2+2y2)dxdy=xy,y(−3)=3 find the following: (a) The coefficient functions...
(1 point) Given the following initial value problem (x2+2y2)dxdy=xy,y(−3)=3 find the following: (a) The coefficient functions are M(x,y)= and N(x,y)= . (Please input values for both boxes.) (b) The separable equation using a substitution of y=ux, is dx+ du=0 (Separate the variables with x with dx only and u with du only.) (Please input values for both boxes.) (c) The implicit solution is x= I just need part C.
1) Solve the given differential equation by using an appropriate substitution. The DE is a Bernoulli...
1) Solve the given differential equation by using an appropriate substitution. The DE is a Bernoulli equation. x dy/dx +y= 1/y^2 2)Consider the following differential equation. (25 − y2)y' = x2 Let f(x, y) = x^2/ 25-y^2. Find the derivative of f. af//ay= Determine a region of the xy-plane for which the given differential equation would have a unique solution whose graph passes through a point (x0, y0) in the region. a) A unique solution exists in the region consisting...
Consider the following statements. (i) The differential equation y′ + P(x) y  =  Q(x) has the...
Consider the following statements. (i) The differential equation y′ + P(x) y  =  Q(x) has the form of a linear differential equation. (ii) All solutions to y′  =  e^(sin(x^2 + y)) are increasing functions throughout their domain. (iii) Solutions to the differential equation y′  =   f (y) may have different tangent slope for points on the curve where y  =  3, depending on the value of x
ADVERTISEMENT
Need Online Homework Help?

Get Answers For Free
Most questions answered within 1 hours.

Ask a Question
ADVERTISEMENT