Homework Answers
Solve x′ =2x+y, x(0)=1 y′ =3x+4y, y(0)=0
Solve x′ =2x+y, x(0)=1 y′ =3x+4y, y(0)=0
(10 point) Solve the following initial value problems. a) y"+ 4y' + 8y = 40cos(2x), y(0)...
(10 point) Solve the following initial value problems. a) y"+ 4y' + 8y = 40cos(2x), y(0) = 8, y'(0) = 0 b) y" + 6y' + 13y = 12e-3xsin(2x), y(0) = 0, y'(0) = 0 (10 point) Find a general solution of each of the following nonhomogeneous equations. a) y" + 4y = 12x−8cos(2x) b) y(4)− 4y" = 16+32sin(2x)
Solve the initial value problem 2x+y-bxy'+4y=0 Y()=0 ; y'C1=252
Solve the initial value problem 2x+y-bxy'+4y=0 Y()=0 ; y'C1=252
Solve: y" + 4y = 8 sin x. O y = A sin 2x + B...
Solve: y" + 4y = 8 sin x. O y = A sin 2x + B cos 2x + (8/3) sin x O y = Ae^(2x) + Be^(-2x) y = A sin 2x + B cos 2x O y = A sin 2x + B cos 2x + sin x
Use the reduction of order method to solve the following problem given one of the solution y1. (a) (x^2 - 1)y'' -2xy' +2y = 0 ,y1=x (b) (2x+1)y''-4(x+1)y'+4y=0 ,y1=e^2x (c) (x^...
Use the reduction of order method to solve the following problem given one of the solution y1. (a) (x^2 - 1)y'' -2xy' +2y = 0 ,y1=x (b) (2x+1)y''-4(x+1)y'+4y=0 ,y1=e^2x (c) (x^2-2x+2)y'' - x^2 y'+x^2 y =0, y1=x (d) Prove that if 1+p+q=0 than y=e^x is a solution of y''+p(x)y'+q(x)y=0, use this fact to solve (x-1)y'' - xy' +y =0
Find an integrating factor of the form x"y" and solve the equation. (2x y-9y)dx + (4y -9x)dy 0 by multiplying b...
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...
Solve the following system of equations. 2x+4y = 8 3x + 4y = 16 x =...
Solve the following system of equations. 2x+4y = 8 3x + 4y = 16 x = 0 Olo X y = -1
Homogenous equation 1. (2x – y) y = 4y – 3x, y(0) = 2
Homogenous equation
1. (2x – y) y = 4y – 3x, y(0) = 2
Solve the systems of equations by substitution #11 2x-y-2 3x+4y-6 Solve each system by elimination or...
Solve the systems of equations by substitution #11 2x-y-2 3x+4y-6 Solve each system by elimination or by any convenient method #13 a) 3x+4y-1 2x-3y-12 b) -4x+3y--!5 3x-2y-4
3) Solve the initial value problem. a) nie - 2x(y2 – 2y) = 0, with y(0)...
3) Solve the initial value problem. a) nie - 2x(y2 – 2y) = 0, with y(0) = 4 b) (-4y cos x + 4 sin I Cos I + sec? x)dx + (4y - 4 sin x)dy = 0, with y ) = 1
Solve the initial value problem 2x+y-bxy'+4y=0 Y()=0 ; y'C1=252
Solve: y" + 4y = 8 sin x. O y = A sin 2x + B cos 2x + (8/3) sin x O y = Ae^(2x) + Be^(-2x) y = A sin 2x + B cos 2x O y = A sin 2x + B cos 2x + sin x
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...
Solve the following system of equations. 2x+4y = 8 3x + 4y = 16 x = 0 Olo X y = -1
Homogenous equation
1. (2x – y) y = 4y – 3x, y(0) = 2
Solve the systems of equations by substitution #11 2x-y-2 3x+4y-6 Solve each system by elimination or by any convenient method #13 a) 3x+4y-1 2x-3y-12 b) -4x+3y--!5 3x-2y-4
3) Solve the initial value problem. a) nie - 2x(y2 – 2y) = 0, with y(0) = 4 b) (-4y cos x + 4 sin I Cos I + sec? x)dx + (4y - 4 sin x)dy = 0, with y ) = 1
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