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4 points) Write the equation in the form y-f(u/z) then use the substitution y zu to...
The equation 4zy + z² + y2 4y can be written in the form y =...
The equation 4zy + z² + y2 4y can be written in the form y = f(y/2). Le it is homogeneous so we can use the substitution y/z to obtain a separable equation with dependent variable u = Introducing this substitution and using the fact that y zu' + u we can write (.) as y = Du' +u = f(u) where f(u) Separating variables we can write the equation in the form dr g(u) du I where g(u) An...
The equation y' 6x2 + 3y2 ту can be written in the form y' = f(y/x),...
The equation y' 6x2 + 3y2 ту can be written in the form y' = f(y/x), i.e., it is homogeneous, so we can use the substitution u = y/x to obtain a separable equation with dependent variable u= u(x). Introducing this substitution and using the fact that y' = ru' + u we can write (*) as y' = xu'+u = f(u) where f(u) = Separating variables we can write the equation in the form dr g(u) du = where...
(1 point) The equation z2 can be written in the form y'-f(y/z), ie., it is homogeneous,...
(1 point) The equation z2 can be written in the form y'-f(y/z), ie., it is homogeneous, so we can use the substitution u-y/z to obtain a separable equation with dependent variable Introducing this substitution and using the fact that y' zuu we can write (*) as u u- f(u) where f(u) Separating variables we can write the equation in the form dz where g(u)- An implicit general solution with dependent variable u can be written in the form In(z) Transforming...
(1 point) The equation 3ry2r 2y2 (*) can be written in the form y f(y/x), ie.,...
(1 point) The equation 3ry2r 2y2 (*) can be written in the form y f(y/x), ie., it is homogeneous, so we can use the substitution u = y/x to obtain a separable equation with dependent variable uu(x. Introducing this substitution and using the fact that y' ru' u we can write () as y xu'w = f(u) where f(u) Separating variables we can write the equation in the form da np (n)6 where g(u) = An implicit general solution with...
(15 points) The equation 5xy + 2x2 + 2y2 5y (*) .22 can be written in...
(15 points) The equation 5xy + 2x2 + 2y2 5y (*) .22 can be written in the form y' = f(y/2), i.e., it is homogeneous, so we can use the substitution u=y/2 to obtain a separable equation with dependent variable u = u(x). Introducing this substitution and using the fact that y' = ru' + u we can write (*) as y' = xu'+u = f(u) where f(u) = Separating variables we can write the equation in the form du...
HW06: Problem 2 Previous Problem Problem List Next Problem (1 point) The equation бх? + Зу...
HW06: Problem 2 Previous Problem Problem List Next Problem (1 point) The equation бх? + Зу (*) ху can be written in the form y = f(y/x), i.e., it is homogeneous, so we can use the substitution u = equation with dependent variable u = u(x). yx to obtain a separable Introducing this substitution and using the fact that y xu' +u we can write (*) as = У = xu' u = f(u) where f(u) Separating variables we can...
(1 point) Consider the first order separable equation y = 16xy(1+2x51/3 An Implicit general solution can...
(1 point) Consider the first order separable equation y = 16xy(1+2x51/3 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) e (1+2x^6)^(4/3) Next find the explicit solution of the initial value problem y(0) = 5
(1 point) f(az +by), ie the RHS is a inear function of z and y We...
(1 point) f(az +by), ie the RHS is a inear function of z and y We wil use the substtution oaz+ by to find an impict general solution In case an equation is in the form +yo sove the initial value problem. The right hand side of the following first order problem is a linear function of az and y Use the substitution sin(a+) We obtain the following separable equation in the varables z and t 1-sin and use cos...
Consider the first order separable equation y(1 + 53*) 1/3 An implicit general solution can be...
Consider the first order separable equation y(1 + 53*) 1/3 An implicit general solution can be written in the form yCf(x) for some function f(x) with an arbitrary constant. Here f(x) Next find the explicit solution of the initial value problem y(0) = 3 y =
sef (1 point) Consider the first order separable equation y' = 45x®y(1 +520)1/2 An explicit general...
sef
(1 point) Consider the first order separable equation y' = 45x®y(1 +520)1/2 An explicit general solution can be written in the form y=Cf(x) for some function f(x) with Can arbitrary constant. Here f(x) = Next find the explicit solution of the initial value problem y(0) = 1 y=
The equation 4zy + z² + y2 4y can be written in the form y = f(y/2). Le it is homogeneous so we can use the substitution y/z to obtain a separable equation with dependent variable u = Introducing this substitution and using the fact that y zu' + u we can write (.) as y = Du' +u = f(u) where f(u) Separating variables we can write the equation in the form dr g(u) du I where g(u) An...
The equation y' 6x2 + 3y2 ту can be written in the form y' = f(y/x), i.e., it is homogeneous, so we can use the substitution u = y/x to obtain a separable equation with dependent variable u= u(x). Introducing this substitution and using the fact that y' = ru' + u we can write (*) as y' = xu'+u = f(u) where f(u) = Separating variables we can write the equation in the form dr g(u) du = where...
(1 point) The equation z2 can be written in the form y'-f(y/z), ie., it is homogeneous, so we can use the substitution u-y/z to obtain a separable equation with dependent variable Introducing this substitution and using the fact that y' zuu we can write (*) as u u- f(u) where f(u) Separating variables we can write the equation in the form dz where g(u)- An implicit general solution with dependent variable u can be written in the form In(z) Transforming...
(1 point) The equation 3ry2r 2y2 (*) can be written in the form y f(y/x), ie., it is homogeneous, so we can use the substitution u = y/x to obtain a separable equation with dependent variable uu(x. Introducing this substitution and using the fact that y' ru' u we can write () as y xu'w = f(u) where f(u) Separating variables we can write the equation in the form da np (n)6 where g(u) = An implicit general solution with...
(15 points) The equation 5xy + 2x2 + 2y2 5y (*) .22 can be written in the form y' = f(y/2), i.e., it is homogeneous, so we can use the substitution u=y/2 to obtain a separable equation with dependent variable u = u(x). Introducing this substitution and using the fact that y' = ru' + u we can write (*) as y' = xu'+u = f(u) where f(u) = Separating variables we can write the equation in the form du...
HW06: Problem 2 Previous Problem Problem List Next Problem (1 point) The equation бх? + Зу (*) ху can be written in the form y = f(y/x), i.e., it is homogeneous, so we can use the substitution u = equation with dependent variable u = u(x). yx to obtain a separable Introducing this substitution and using the fact that y xu' +u we can write (*) as = У = xu' u = f(u) where f(u) Separating variables we can...
(1 point) Consider the first order separable equation y = 16xy(1+2x51/3 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) e (1+2x^6)^(4/3) Next find the explicit solution of the initial value problem y(0) = 5
(1 point) f(az +by), ie the RHS is a inear function of z and y We wil use the substtution oaz+ by to find an impict general solution In case an equation is in the form +yo sove the initial value problem. The right hand side of the following first order problem is a linear function of az and y Use the substitution sin(a+) We obtain the following separable equation in the varables z and t 1-sin and use cos...
Consider the first order separable equation y(1 + 53*) 1/3 An implicit general solution can be written in the form yCf(x) for some function f(x) with an arbitrary constant. Here f(x) Next find the explicit solution of the initial value problem y(0) = 3 y =
sef
(1 point) Consider the first order separable equation y' = 45x®y(1 +520)1/2 An explicit general solution can be written in the form y=Cf(x) for some function f(x) with Can arbitrary constant. Here f(x) = Next find the explicit solution of the initial value problem y(0) = 1 y=
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