The differemtial equation
has an implicit general solution of the form F(x,y)= K, where K is an arbitary constant. In fact, because the differential equation is separable, we can deifine 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)=????
Homework Answers
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The differemtial equation
has an implicit general solution of the form F(x,y)= K, where K
is...
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(1 point) Consider the first order separable equation y' y(y- 1) An implicit general solution can...
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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...
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4 points) Write the equation in the form y-f(u/z) then use the substitution y zu to...
4 points) Write the equation in the form y-f(u/z) then use the substitution y zu to find an implicit general solution. Then solve the initial value problem. The resulting differential equation in z and u can be written as zu' Separating variables we arrive at Separating variables and and simplifying the solution can be written in the form u2 1-Cf(x) where C is an arbitrary constant and which is separable. da du f(x) ias problem is
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(1 point) Consider the first order separable equation y' y(y- 1) An implicit general solution can be written in the form e + h(x, y) Find an explicit solution of the initial value problem y(0)3 C where h(z, y) ( y)
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...
Determine whether the given relation is an implicit solution to the given differential equation. Assume that the relationship does define y implicitly as a function of x and use implicit differentiation. -xy -y dy e +y=x+3, dx -wy+X -xy- dy V equivalent to dx Va solution to the differential equation. Therefore, e+ yx+3 y+x Applying implicit differentiation to the equation gives which
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 =
Solve the equation (3x2y-dx + y - 4x®y-dy=0 An implicit solution in the form F(x,y)=Cis-C, where is an arbitrary constant, and (Type an expression using x and y as the variables ) by multiplying by the integrating factor
Find an integrating factor of the form x"y" and solve the equation. (2x y-9y)dx + (4y -9x)dy 0 by multiplying by the integrating factor. An implicit solution in the form F(x,y) C is C, where C is an arbitrary constant, and (Type an expression using x and y as the variables.)
Find an integrating factor of the form x"y" and solve the equation. (2x y-9y)dx + (4y -9x)dy 0 by multiplying by the integrating factor. An implicit solution in the...
4 points) Write the equation in the form y-f(u/z) then use the substitution y zu to find an implicit general solution. Then solve the initial value problem. The resulting differential equation in z and u can be written as zu' Separating variables we arrive at Separating variables and and simplifying the solution can be written in the form u2 1-Cf(x) where C is an arbitrary constant and which is separable. da du f(x) ias problem is
If = Q, where Q is a function of y only, then the differential equation M + Ny = 0 has an integrating factor of the form +(y) = es Q(u) dy Find an integrating factor and solve the given equation. ydx + (3xy - e-39) dy=0 Enclose arguments of functions in parentheses. For example, sin (22) To enter y in text mode, type (ly) or abs(y). Use multiplication sign in all cases of multiplication. The integrating factor is (y)...
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