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(1 point) We know that y(x) 72 is a solution to the differential equation Dy -...
(1 point) We know that y(x) = ** is a solution to the differential equation y...
(1 point) We know that y(x) = ** is a solution to the differential equation y - 12y - 64y = 0 for x € (-0,00) Use the method of reduction of order to find the second solution to y - 12y - 64 y = 0 for x € (-0, 0). (a) After you reduce the second order equation by making the substitution w = C', you get a first order equation of the form w = f(x, w)...
(1 point) The differential equation dx has r4 as a solution. Applying reduction order we set...
(1 point) The differential equation dx has r4 as a solution. Applying reduction order we set Y2-uz" Then (using the prime notation for the derivatives) So, plugging 32 into the left side of the differential equation, and reducing, we get The reduced form has a common factor of r5 which we can divide out of the equation so that we have ru" + u0 Since this equation does not have any u terms in it we can make the substitution...
(1 point) Given a second order inear homogeneous differential equation az(x) + we know that a...
(1 point) Given a second order inear homogeneous differential equation az(x) + we know that a fundamental set for this ODE consists of a pair nearly ndependent solutions . linearly independent solution We can find using the method et reduction of (2) + Golly=0 But there are times when only one functional and we would e nd a con First under the necessary assumption the a, (2) we rewrite the equation as * +++ (2) - Plz) - ) Then...
(1 point) A Bernoulli differential equation is one of the form dy dc + P(x)y= Q(x)y"...
(1 point) A Bernoulli differential equation is one of the form dy dc + P(x)y= Q(x)y" Observe that, if n = 0 or 1, the Bernoulli equation is linear. For other values of n, the substitution u = yl-n transforms the Bernoulli equation into the linear equation du dr +(1 – n)P(x)u = (1 - nQ(x). Consider the initial value problem xy + y = 3xy’, y(1) = -8. (a) This differential equation can be written in the form (*)...
(15 points) A Bernoulli differential equation is one of the form dy dar + P(x)y= Q(x)y"....
(15 points) A Bernoulli differential equation is one of the form dy dar + P(x)y= Q(x)y". Observe that, if n = 0 or 1, the Bernoulli equation is linear. For other values of n, the substitution u=yl-n transforms the Bernoulli equation into the linear equation du + (1 - n)P(x) = (1 - nQ(x). dx Use an appropriate substitution to solve the equation xy' +y=2xy? and find the solution that satisfies y(1) = 1.
Consider the homogeneous linear third order equation A) xy'''−xy'' + y'−y = 0 Given...
Consider the homogeneous linear third order equation A) xy'''−xy'' + y'−y = 0 Given that y1(x) = e^x is a solution. Use the substitution y = u*y1 to reduce this third order equation to a homogeneous linear second order equation in the variable w = u'. You do not need to solve this second order equation. B.) xy''' + (1−x)y'' + xy'−y = 0. Given that y1(x) = x is a solution. Use the substitution y =...
The indicated function y(x) is a solution of the given differential equation. Use reduction of order...
The indicated function y(x) is a solution of the given differential equation. Use reduction of order or formula (5) in Section 4.2, re-SP(x) dx as instructed, to find a second solution y2(x). XY" + y = 0; Y- In x
1. 10 points Given y(x) x 'is a solution to the differential equation x’y"+ 6xy'+6y=0 (x...
1. 10 points Given y(x) x 'is a solution to the differential equation x’y"+ 6xy'+6y=0 (x > 0), find a second linearly independent solution using reduction of order.
Solve the homogeneous differential equation -y d) dy 0. (Note: Some algebraic manipulation goes into putting...
Solve the homogeneous differential equation -y d) dy 0. (Note: Some algebraic manipulation goes into putting your answer into the form below.) (1 point) Use substitution to find the general solution of the differential equation (2-y) dx + x dy = 0. (Use C to denote the arbitrary constant and Inl input if using In.) help (formulas)
Consider the differential equation dy/dx = (y-1)/x.
Consider the differential equation dy/dx = (y-1)/x. (a) On the axes provided, sketch a slope field for the given differential equation at the nine points indicated. (b) Let y = f (x) be the particular solution to the given differential equation with the initial condition f (3) = 2. Write an equation for the line tangent to the graph of y= f (x) at x = 3. Use the equation to approximate the value of f (3.3). (c) Find the particular solution y...
(1 point) We know that y(x) = ** is a solution to the differential equation y - 12y - 64y = 0 for x € (-0,00) Use the method of reduction of order to find the second solution to y - 12y - 64 y = 0 for x € (-0, 0). (a) After you reduce the second order equation by making the substitution w = C', you get a first order equation of the form w = f(x, w)...
(1 point) The differential equation dx has r4 as a solution. Applying reduction order we set Y2-uz" Then (using the prime notation for the derivatives) So, plugging 32 into the left side of the differential equation, and reducing, we get The reduced form has a common factor of r5 which we can divide out of the equation so that we have ru" + u0 Since this equation does not have any u terms in it we can make the substitution...
(1 point) Given a second order inear homogeneous differential equation az(x) + we know that a fundamental set for this ODE consists of a pair nearly ndependent solutions . linearly independent solution We can find using the method et reduction of (2) + Golly=0 But there are times when only one functional and we would e nd a con First under the necessary assumption the a, (2) we rewrite the equation as * +++ (2) - Plz) - ) Then...
(1 point) A Bernoulli differential equation is one of the form dy dc + P(x)y= Q(x)y" Observe that, if n = 0 or 1, the Bernoulli equation is linear. For other values of n, the substitution u = yl-n transforms the Bernoulli equation into the linear equation du dr +(1 – n)P(x)u = (1 - nQ(x). Consider the initial value problem xy + y = 3xy’, y(1) = -8. (a) This differential equation can be written in the form (*)...
(15 points) A Bernoulli differential equation is one of the form dy dar + P(x)y= Q(x)y". Observe that, if n = 0 or 1, the Bernoulli equation is linear. For other values of n, the substitution u=yl-n transforms the Bernoulli equation into the linear equation du + (1 - n)P(x) = (1 - nQ(x). dx Use an appropriate substitution to solve the equation xy' +y=2xy? and find the solution that satisfies y(1) = 1.
The indicated function y(x) is a solution of the given differential equation. Use reduction of order or formula (5) in Section 4.2, re-SP(x) dx as instructed, to find a second solution y2(x). XY" + y = 0; Y- In x
1. 10 points Given y(x) x 'is a solution to the differential equation x’y"+ 6xy'+6y=0 (x > 0), find a second linearly independent solution using reduction of order.
Solve the homogeneous differential equation -y d) dy 0. (Note: Some algebraic manipulation goes into putting your answer into the form below.) (1 point) Use substitution to find the general solution of the differential equation (2-y) dx + x dy = 0. (Use C to denote the arbitrary constant and Inl input if using In.) help (formulas)
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