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Problem 8
a. y" + 4y - sin (2 t) + + -1 b. 4y" - 4y + y = 164/2 8. Evaluate the triple integral SSS w 2x DV, where W is the solid in three-dimensional region bounded by the Surfaces 2 = x+y?, 2:21+y), 21
Solve the following system of equations. 2x+4y = 8 3x + 4y = 16 x = 0 Olo X y = -1
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 by the Method of Undetermined Coefficients. 1. " - 3y' - 4y = 3e2x (ans. y = C1e4x + cze* - e2x) 2. " - 4y = 4e3x (ans. y = C1 e - 2x + C2 e 2x + 4/5 e3x) 3. 2y" + 3y' + y = x2 + 3 sin x (ans. y = ci e-* + C2 e-x/2 + x2 - 6x + 14 - 3/10 sin x- 9/10 cos x) 4. Y" + y'...
a. Find a particular solution to the nonhomogeneous differential equation y" + 4y = cos(2x) + sin(2x) b. Find the most general solution to the associated homogeneous differential equation. Use cand in your answer to denote arbitrary constants. c. Find the solution to the original nonhomogeneous differential equation satisfying the initial conditions y(0) = 8 and y'(0) = 4
7. Given that y(x) = sin 2x is a particular solution to y" + 2y + 4y - 4 cos 2x = 0, find the general solution.
Find the general solution of y” + 4y' + 5y = 0. Select one: • a. y = {-2x (cos(x) + sin(x)) b. y = e-24 (A cos(x) + B sin(x)) c.y = Cje-2x (cos(x) + sin(x)) O d. y = e*(A cos(2x) + B sin(2x))
Verify the identity: sin 2x/sin x - cos 2x/cos x = sec x Solve the equation tan theta = Squareroot 3.
Help with question 6
7. Use variation of parameters and solve y"+4y = cosec(2x) sin(x) Given y is a solution to t’y"+ xy + (x² -0.25)y=0, use reduction of 8. order and determine the general solution. -End of Paper- 6. According to Newton's law of cooling, the rate at which a substance cools in moving air is proportional to the difference between the temperature of the body and that of the air. If the temperature of air is 300K (Kelvin)...
Solve x′ =2x+y, x(0)=1 y′ =3x+4y, y(0)=0