Question

1242) y=A x ln(x) + B x + F is the particular solution of the second-order linear DEQ: xy'' =9 where y'=3 at the point (3,3). Determine A,B,F. y=A x ln(x) + B x + F is also called an explicit solution. Is the DEQ separable, exact, 1st-order linear, Bernouli? Please help solve this question. Find A,B,and F.

Answer #1

1250) y=Aexp(Bx)+Fexp(Gx) is the particular solution of
the second order linear differential equation:
(y'') + ( 2y') + (-24y) = 0, subject to the boundary conditions:
y=4, and y'=1 when x=0. Find A,B,F, and G, where B>G.

1220) y=Ax+Dx^B is the particular solution of the
first-order homogeneous DEQ: (x-y) = 4xy'. Determine A,B, & D
given the boundary conditions: x=7 and y=4.

1249) The solution of some second order linear DEQ is
exp(-1x)[5sin(3x)+ 2cos(3x)] which can also be expressed as
A*exp(-D*x)*sin(F*x+G). Determine A,D,F, and G (degrees). ans:4
1252) y=(C1)exp(Ax)+(C2)exp(Bx)+F+Gx is the general solution of the second order linear differential equation: (y'') + ( -8y') + ( -9y) = ( -8) + ( 3)x. Find A,B,F,G, where A>B. This exercise may show "+ (-#)" which should be enterered into the calculator as "-#", and not "+-#". ans:4

1218) y=Ax+Cx^B is the general solution of the first-order homogeneous DEQ: (x-y) dx - 2x dy = 0. Determine A and B. Also, include a manual solution in your portfolio. ans:2
1220) y=Ax+Dx^B is the particular solution of the first-order homogeneous DEQ: (x-y) = 2xy'. Determine A,B, & D given the boundary conditions: x=7 and y=5. Include a manual solution in your portfolio. ans:3

Let f (x, y) = (x −
9) ln(xy).
(a)
Find the the critical point (a, b). Enter the
values of a and b (in that order) into the answer
box below, separated with a comma.
(b)
Classify the critical point.
(A) Inconclusive (B) Relative Maximum (C) Relative Minimum (D)
Saddle Point

Problem 1.
(1 point)
Find the critical point of the function
f(x,y)=−(6x+y2+ln(|x+y|))f(x,y)=−(6x+y2+ln(|x+y|)).
c=?
Use the Second Derivative Test to determine whether it is
A. a local minimum
B. a local maximum
C. test fails
D. a saddle point

1252) y=(C1)exp(Ax)+(C2)exp(Bx)+F+Gx is the general solution of
the second order linear differential equation:
(y'') + ( -9y') + ( 20y) = ( -9) + ( -8)x. Find A,B,F,G, where
A>B. This exercise may show "+ (-#)" which should be enterered into
the calculator as "-#", and not "+-#". ans:4

(61). (Bernoulli’s Equation): Find the general solution of the
following first-order differential equations:(a) x(dy/dx)+y=
y^2+ln(x) (b) (1/y^2)(dy/dx)+(1/xy)=1

1252) y=(C1)exp(Ax)+(C2)exp(Bx)+F+Gx is the general solution of
the second order linear differential equation:
(y'') + ( -4y') + ( 3y) = ( 2) + ( -7)x. Find A,B,F,G, where
A>B.

solve for y:
1. dy/dx= xe^y separable
2. x(dy/dx)+3y=x^2 when y(5)=0 1st order linear

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